Prospects of toxoplasmosis control by cat vaccination

Journal Pre-proof Prospects of toxoplasmosis control by cat vaccination Axel A. Bonacic Marinovic, Marieke Opsteegh, Huifang Deng, Anita W.M. Suijkerbuijk, Paul F. van Gils, Joke van der Giessen

PII:

S1755-4365(19)30059-3

DOI:

https://doi.org/10.1016/j.epidem.2019.100380

Reference:

EPIDEM 100380

To appear in:

Epidemics

Received Date:

16 April 2019

Revised Date:

18 November 2019

Accepted Date:

1 December 2019

Please cite this article as: Axel A. Bona\v{c}i\’c Marinovi\’c, Marieke Opsteegh, Huifang Deng, Anita W.M. Suijkerbuijk, Paul F. van Gils, Joke van der Giessen, Prospects of toxoplasmosis control by cat vaccination, (2019), doi: https://doi.org/10.1016/j.epidem.2019.100380

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Prospects of toxoplasmosis control by cat vaccination. Axel A. Bonaˇci´c Marinovi´c1 , Marieke Opsteegh1 , Huifang Deng1 , Anita W. M. Suijkerbuijk1 , Paul F. van Gils1 and Joke van der Giessen1 National Institute for Public Health and the Environment, Bilthoven, The Netherlands

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1

E-mail: [email protected]

November 18, 2019

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Abstract

Intro: Toxoplasmosis has high disease burden in the Netherlands and in the rest of Europe. It can be acquired directly by ingestion of Toxoplasma gondii (T. gondii) oocysts shed by

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infected cats, or indirectly via consumption of undercooked meat from infected livestock. Cat vaccination has been proposed for reducing oocyst-acquired human infections but it remains unclear whether such an intervention can be effective. In this study we quantified

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the effects of using cat vaccination on reducing oocyst-originated T. gondii human infections. Method: By using a disease dynamics compartmental model for T. gondii infections in cats and mice we studied the effects of a hypothetical cat vaccine on the presence of T.

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gondii oocysts in the environment. A fitted dose response model was used to assess the effect of oocyst reduction on the expected human infections. Results: For rats, mice and pigs, and possibly intermediate hosts in general, ingestion of one oocyst provides 30%-60% probability of T. gondii infection. Assuming a favourable ideal

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scenario where vaccination completely prevents oocyst shedding and predation rate is of one mouse per week per cat, eight cats can be left susceptible in order to achieve elimination and stop oocyst-originated transmission, independent of the total cat population. Considering

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populations of 1000, 100, 50 and 20 cats, cat vaccination coverage of 94%, 68%, 54% and 35%, respectively, would reduce expected oocyst-originated human cases by 50%. Conclusion: For attaining elimination of oocyst-originated human infections, only few cats may remain unvaccinated, regardless of the cat-population size, and only a few more cats may remain unvaccinated for reducing infections substantially. Such vaccination coverages can in practice be achieved only when small cat-populations are considered, but in larger cat-populations the large efficacy and vaccination coverage needed are unfeasible.

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1

Introduction

Toxoplasmosis is caused by the protozoan parasite Toxoplasma gondii. This parasite can infect a wide range of animals, from birds to mammalian animals such as cats, sheep, pigs and cattle, as well as humans. Infection can be acquired by ingestion of T. gondii oocysts present in the environment, by ingestion of tissue T. gondii cysts present in muscles and tissues of infected animals, or by vertical transmission during gestation (Tenter et al., 2000). T. gondii can complete its life cycle only in felids (definitive hosts), including domestic cats. After infection, cats shed

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millions of oocysts in their faeces for up to three weeks (Dabritz and Conrad, 2010). These oocysts can remain viable in the environment for months (Frenkel et al., 1975; Dum`etre and Dard´e, 2003).

Most infections in humans occur either by eating under-cooked infected meat or by exposure to oocysts in the environment, often leading to an asymptomatic infection or mild flu-like

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symptoms (Elmore et al., 2010), but potentially leading to the development of ocular toxoplas-

mosis later in life (e.g., Weiss and Dubey, 2009). Toxoplasmosis is also well-known as a cause of congenital disease as infection during pregnancy can lead to abortion, stillbirth and serious dis-

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orders in newborns such as hydrocephalus, microcephalus and chorioretinitis in later life (Weiss and Dubey, 2009). As a consequence of these serious health risks, toxoplasmosis is one of the

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most important food-borne diseases in terms of burden of disease in the Netherlands and Europe (Bouwknegt et al., 2014; Havelaar et al., 2015; Mangen et al., 2017). In order to reduce the burden of disease, strategies are needed to prevent congenital and acquired T. gondii infection in the general population. Currently, there is much debate of the

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measures to be taken to achieve this goal at certain costs. Opsteegh et al. (2015) described that cat vaccination and freezing of meat destined for raw or under-cooked consumption are potential strategies. Although a vaccine against T. gondii infection has not been specifically developed

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for cats yet, cat vaccination has been studied experimentally as means of preventing T. gondii exposure in swine farms with promising results (Mateus-Pinilla et al., 1999). Cat vaccination

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has also been studied in the context of T. gondii infection dynamics models (e.g., Mateus-Pinilla et al., 2002; Arenas et al., 2010; Sykes and Rycht´aˇr, 2015). However, these studies considered a single mechanism for the force of infection, where there is no distinction between infections originated by ingestion of oocysts and ingestion of tissue cysts by eating infected prey. Prey have different mortality rates than the rate of inactivation of oocysts, and cats are more susceptible to infection by ingestion of tissue cysts from infected prey than to infection by ingestion of oocysts (Dubey, 2006). L´elu et al. (2010) presented a model including definitive and intermediate host 2

life cycles of T. gondii, i.e., cats (definitive hosts) become infected not only by direct contact with infected environment (oocysts), but also by eating prey (intermediate hosts, e.g., mice) which in turn have been infected by contact with oocysts in the environment. The aim of that study was to provide a more accurate description of transmission due to the full life-cycle of T. gondii, however, L´elu et al. (2010) did not use the model to study vaccination strategies. A similar scenario has been studied with an agent-based model by Jiang et al. (2012), which also included vertical transmission. The model from L´elu et al. (2010) was extended further by Turner et al. (2013), including additional parameters, such as mice behavioural change after

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infection, to study the effects of cat vaccination and rodent control measures on the potential reduction of the disease incidence in sheep.

We studied the effect of cat vaccination on reducing the risk of oocyst-originated human T. gondii infections in the Netherlands. By using a compartmental model based on the definitive-

and intermediate-host framework described above we calculated the presence of oocysts in the

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environment under various degrees of vaccination coverage. Subsequently, our findings were

combined with a calculated dose-response function to assess the potential reduction in the risk

Methods

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2

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of infection for humans.

To study the effect of cat vaccination in reducing the risk of human toxoplasmosis by oocyst exposure we first employed a disease dynamics compartment model which considers the direct-

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and indirect-host life cycles for T. gondii and infection of humans via environmental transmission. Two modelling approaches were used regarding how infections occur via the contaminated environment. One approach considers a fixed probability of infection, given contact with con-

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taminated patches of environment (L´elu et al., 2010), which can be interpreted as if oocysts are clustered in the environment and always cause infection, independent of the dose, as long as they are ingested. The other approach considers the probability of infection to be proportional to the

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oocyst abundance (Arenas et al., 2010; Turner et al., 2013), which can be interpreted as oocysts being homogeneously distributed in the environment and the more there are the higher the probability of infection. Model parameter values found in the literature were used, predominantly from L´elu et al. (2010), and some were modified to fit those parameters corresponding to the current situation in the Netherlands (details in Table 1). We established a dose-response relation between number of oocysts ingested and the probability of infection in humans. Reduction of

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the force of infection in humans was studied with a series of vaccination coverage scenarios. The reduction was evaluated when the models reached dynamic equilibrium. Various cat population sizes using the two modelling approaches on infection via the contaminated environment were considered.

2.1

Dynamic model of T. gondii infection

We employed a compartmental model of infection transmission dynamics which considers the definitive-host (cats) and intermediate-host (mice) life cycles of T. gondii, respectively indicated

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by subindices 1 and 2 (Fig. 1). A subindex i is used when the description of a variable or

parameter from our model applies to both kinds of hosts. Despite the more details included in

the model from Turner et al. (2013), some of its extra parameters such as mouse behavioural changes after infection remain uncertain. Therefore, we built up our model based on that of L´elu et al. (2010).

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Our model considers susceptible, infectious and recovered/resistant compartments (S1 , I1

and R1 , respectively) describing the disease dynamics in a total population of N1 cats. Cats

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become infected by ingesting infectious oocysts shed in the environment by other infectious cats or by ingesting tissue cysts by eating infected prey. Infectious cats shed oocysts for a couple of weeks and then become recovered, remaining protected for life from a new infection.

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During infection, cats contaminate the environment with infectious oocysts contained in their faeces (Tenter et al., 2000). Although oocysts need one or two days after being excreted to sporulate and become infectious in the environment, in the model that delay is neglected given

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the much longer time that matured infectious oocysts remain viable (three months or more). The contamination of the environment is represented by the compartment E (described further in § 2.1.3). The disease dynamics for total population of N2 mice are described by susceptible and

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infected compartments (S2 and I2 , respectively). Infected mice remain infectious for life since tissue cysts remain viable and cats become infected after eating infected animals. Recovered cats also have persistent tissue cysts, which makes them infectious if eaten, but in this study we

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neglect the possibility as cats are mostly predators rather than prey. The various parameters considered in the model are explained in the following sections, and

are listed with their respective chosen value and reference in Table 1.

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b 1v

b1(1-v)

I1

2

m1

l I1

b 1E

m1

d

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b 2E

Figure 1:

b2

m2

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m2

1-E

S2

na

I2

m1

re

gp

(N

E

R1

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2,N

1)

I2/N

g

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S1

Compartmental model of T. gondii infection including definitive hosts (cats) and

intermediate hosts (mice). The compartments in the model are susceptible cats (S1 ), infected

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cats (I1 ), recovered cats (R1 ), susceptible mice (S2 ), infected mice (I2 ), and contaminated environment (E).

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2.1.1

Demographics

Once infected, cats shed oocysts for about two weeks. Then cats recover and stop shedding oocysts, remaining protected and sero-positive for life (Tenter et al., 2000). Consequently, the turnover of the cat population becomes a determinant factor on the incidence of shedding episodes. Therefore, cat population dynamics needs to be appropriately taken into account. The model by L´elu et al. (2010) considers the demographics of cats and mice to have a logistic growth with resource limitations. With this approach, when birth rate (bi ) is larger than death rate (mi ), the population grows until the environmental maximum capacity (Ki ) is reached. At

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this point, the population cannot grow further and mortality is enhanced to a level that balances

out the birth rate, making the latter the driver of the population turnover. This situation may

be correct for mice populations, so we assumed that this is the case. A birth-rate driven cat population turnover may also be appropriate in case of feral cat populations, but in the case

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of more controlled populations such as farms, owners have the tendency to keep their already

grown animals, and cull or give away the newly born animals. It is still reasonable to assume a constant population in this latter situation, but its turnover should be driven by the cat death

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rate. Even at a national scale, the Dutch cat population is not growing significantly fast and the average age of a cat in the Netherlands is 7.7 years (Borst et al., 2011), resulting in significantly slower death rate than the cat birth rate used in the modelling previous studies (e.g., Arenas

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et al., 2010; L´elu et al., 2010; Turner et al., 2013).

We assumed that the cat population is in equilibrium, so its value, N1 , was the same as the carrying capacity number, K1 . The same assumption was made for the mouse population,

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where N2 = K2 . We studied our model assuming various population sizes, namely 1000, 100, 50, 25 and 15 cats, and that the mouse population was 25 times the number of cats to ensure

2.1.2

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enough mice available as prey. Cat vaccination

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For simplicity, we assumed that cats are vaccinated right after birth, before they can get infected or loose any potential maternal antibody protection (Mateus-Pinilla et al., 2002). This provides a best-case scenario analysis in the sense that it is comparable with vaccination occurring at a very high rate, but we focus on the fact that the vaccination coverage ratio can vary, i.e., only a fraction of the cat population is swiftly vaccinated. Therefore, we added vaccination to the original model of L´elu et al. (2010) by assuming that a given fraction (v) of the cat population is born vaccinated, and not that cats are vaccinated at a certain rate (e.g., Turner 6

et al., 2013). A vaccine against T. gondii infection has not been specifically developed for cats yet, so a hypothetical perfect vaccine is considered, with which vaccinated cats are assumed to have complete and lifelong protection against infection and they will not shed oocysts. We performed our analysis with a vaccination ratio v, ranging from 0 to 1. The effects of a partially effective vaccine can be included by simply reducing v in a factor equivalent to the vaccine effectiveness, so without loosing generality we assumed a 100% effective vaccine through our analysis. Contaminated environment

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2.1.3

The environment is contaminated by oocysts contained in the faeces of infectious cats at a rate

λ. A proportion E of the environment is contaminated and oocysts have a death rate d. In the work of Turner et al. (2013), it is argued that the change rate of the contaminated proportion

of the environment proposed by the study of L´elu et al. (2010), E˙ = λI1 (1 − E) − dE, is not

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appropriate, as it would favour cats to shed in places which are not yet contaminated. However, the term criticised as cats avoiding contaminated patches of environment, −λI1 E, really means

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that already contaminated environment does not become “more” contaminated. Therefore, only the clean portion of the environment, with probability (1 − E) of being found, can be contaminated by an infectious cat. The interpretation here is that oocysts are found clustered

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and will infect always, as long as a cluster is found and ingested (with a fixed probability), i.e., infectiousness does not increase if oocysts clusters are larger. Furthermore, the formulation of Turner et al. (2013) allows the variable E to grow further than 1, which is conceptually not

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appropriate for a proportion. However, it is still sensible to think that a heavily contaminated part of the environment (e.g., a defecating site used by 10 shedding cats) could be more infectious than a lightly contaminated one (e.g., a defecating site used by only one shedding cat). Such

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a situation is better described by the formulation of Turner et al. (2013), where E˙ = λI1 − dE . However, it should be interpreted as previously proposed by Arenas et al. (2010), where the whole environment is homogeneously contaminated and E represents a variable proportional to

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the total number of oocysts in the environment. In order to study the effect of vaccination using both approaches described above, we wrote

the environment contamination equation as E˙ = λI1 (1 − ME) − dE,

(1)

where M = 1 when oocysts are considered clustered (model by L´elu et al., 2010), and M = 0 when oocysts are considered homogeneously distributed (model by Turner et al., 2013). Note 7

Table 1: Model parameter values. Parameter

Notation

Value/Distribution

Reference

K1

variable

see text, §2.1.1

Cat mortality rate

m1

(1/7.7)/52 [wk−1 ]

Borst et al. (2011).

Cat birth rate

b1

= m1

see text, §2.1.1

β1

0.54/52 [wk−1 ]

γ

1/2 [wk−1 ]

λ

1/16 [wk−1 ]

Cat population size at equilibrium / carrying

Transmission rate from contaminated environment to

environment by one cat Oocyst shedding rate by one

Dum` etre and Dard´ e (2003).

1 [wk−1 ]

see text, §2.1.4

β2

0.4/52 [wk−1 ]

L´ elu et al. (2010).

prey

K2

variable

see text, §2.1.1

b2

6/52 [wk−1 ]

L´ elu et al. (2010).

m2

2/52 [wk−1 ]

L´ elu et al. (2010).

g

1

Dubey (2006).

v

variable

see text, §2.1.2

p(N2 , N1 )

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Transmission rate from contaminated environment to

re 1/100 [wk−1 ]

d

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Predation rate per cat

et al. (2010).

Cornelissen et al. (2014).

Environment

oocyst death rate

Afonso et al. (2008); L´ elu

2 × 108 [wk−1 ]

ξ infectious cat

decontamination rate /

Dabritz and Conrad (2010).

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Contamination rate of

Afonso et al. (2006, 2008); L´ elu et al. (2010).

cats Cat recovery rate

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capacity

Prey population size at

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equilibrium / carrying capacity

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Birth rate of prey

Mortality rate of prey

Probability of infection when cat consumes infected prey Vaccinated cat ratio

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that these two descriptions and their interpretation are opposite extremes on how contact and infection with oocysts may occur, so a most realistic description approach may be somewhere in between. At low levels of environmental contamination (i.e., small E) both models behave equivalently and they begin to differ as E becomes larger. In order to follow the total number of oocysts in the environment (O) at any time we assumed the equation O˙ = ξI1 − dO, where ξ is the rate at which an infectious cat sheds oocysts. 2.1.4

Predation

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We studied cat vaccination to achieve elimination of T. gondii infections as a function of predation rates in the range of 0 to 1 mouse per week per cat. The rate of predation considered for evaluating the effects of cat vaccination for reducing T. gondii infections was p(N2 , N1 ) = 1

mouse per week per cat. This is the highest value in the range suggested by L´elu et al. (2010)

and it provides a conservative scenario of high force of infection for our study on the effects

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of vaccination, without driving the prey population extinct. For comparison purposes we also perform our calculations assuming that only the simple life cycle of T. gondii takes place, i.e.,

2.1.5

Dynamic model equations

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there is no predation.

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The model is described by the following set of equations:

S˙ 1 = b1 (1 − v)N1 − m1 S1 − β1 ES1

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− g p(N2 , N1 )S1 I2 /N2

I˙1 = − m1 I1 + β1 ES1 + g p(N2 , N1 )S1 I2 /N2 − γI1

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R˙ 1 = b1 vN1 − m1 R1 + γI1 E˙ = λI1 (1 − ME) − dE

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S˙ 2 = b2 N2 − (m2 + (b2 − m2 )N2 /K2 )S2 − β2 ES2 − p(N2 , N1 )N1 S2 /N2 I˙2 = − (m2 + (b2 − m2 )N2 /K2 )I2 + β2 ES2 − p(N2 , N1 )N1 I2 /N2 O˙ = ξI1 − dO

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(2)

These are an adaptation of the set of equations from L´elu et al. (2010) to the assumptions described above. Note that if M = 1, then our equations describe a simplified adaptation of the model from Turner et al. (2013). As humans do not contribute to the T. gondii life cycle, we added the human component later to follow the incidence of human T. gondii infections by contact with contaminated environment (§ 2.4).

2.2

Prospects of elimination

To get an idea on the possibilities of elimination of T. gondii infection within a closed population

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of cats we looked at the basic reproduction number, R0 , which is defined as the expected number

of new infected individuals that one infected individual directly produces when introduced in a

naive population (e.g., Anderson and May, 1991; Diekmann and Heesterbeek, 2000; Diekmann

et al., 2012). The most relevant property of R0 is that an infectious disease is able to prevail only if R0 > 1. By finding the set of parameters which bring R0 below its threshold level one finds

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the conditions under which the disease can be controlled. Defining Nnv = N1 (1 − v), the number of cats in the population which remain non-vaccinated, we computed R0 from the equation from

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L´elu et al. (2010)

2 3 R03 − R0S R0 − R0C = 0. λβ1 Nnv (b1 +γ)d

is the simple life-cycle component representing the reproduction number

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2 = Here, R0S

(3)

3 = without predation involved (p(N2 , N1 ) = 0), and R0C

λβ2 p(N2 ,N1 )gNnv (b1 +γ)db2

is the complex life-cycle

component representing the reproduction number as if transmission occurs only by predation

2.3

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(β1 = 0).

Human dose-response relation

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In order to calculate the incidence of human T. gondii infections in the model, a human doseresponse relation upon oocyst ingestion is needed. Explicit dose-response relation data are available for mice, rats, cats and pigs (Dubey and Frenkel, 1973; Dubey, 1996; Dubey et al.,

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1996, 1997; Dubey, 2006; Cornelissen et al., 2014) as shown in Fig. 2, but not for humans. Mice, rats and pigs are intermediate hosts and their dose-response seems similar (Fig. 2), while that of cats (definitive hosts) is different by orders of magnitude in dose. Therefore, on lack of better knowledge and given that humans are intermediate hosts, we assumed that the human dose-response relation is no different from that known for other intermediate mammalian hosts, i.e., mice, rats and pigs.

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1.0

Study/Animal

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Prob. Infection

D06.mice D73.mice1

0.6

D73.mice2 D96.mice

0.4

D96.pigs

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D96.rats

D97.mice

0.0 100

102

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10−2

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0.2

104

106

Dose (no. oocyst)

Dose-response relation for T. gondii infection by ingesting oocysts. The black line

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Figure 2:

indicates the median dose-response relation estimated. The grey area indicates 95% of the most probable estimates. The dashed line shows the median dose-response curve estimate for

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considering a purely Beta-Binomial distributed probability of infection. The dotted line shows the probability of exposure to at least one oocyst. The coloured dots and lines show doseresponse relations observed in various studies for pigs, rats and mice (mammalian intermediate

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hosts). Each colour represents a different animal and study, as indicated in the legend, where D73, D96, D96.pigs, D97 and D06 correspond to the studies of Dubey and Frenkel (1973), Dubey (1996), Dubey et al. (1996), Dubey et al. (1997) and Dubey (2006), respectively.

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For establishing one dose-response relation with the data from several intermediate host species from various studies, we used a Bayesian framework, which directly provides results with credibility intervals. The Markov chain Monte-Carlo simulations of the model were carried out with the software JAGS (Plummer, 2003), version 4.3. Strictly speaking, the probability of infection is well represented by a confluent hyper-geometric function (Teunis et al., 2008), but it is difficult to implement in the software. We assumed a Beta-Binomial probability distribution for infection given a dose of multiple oocysts (good approximation for large dose values). We approached the region of low doses by multiplying the Beta-Binomial probability by the prob-

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ability of exposure to at least one oocyst (1 − e−dose ), rising from a Poisson distributed dose with mean value as indicated by the dilution. In this way, at low doses the probability of infec-

tion cannot become higher than the probability of exposure. At increasingly large dose values,

1 − e−dose becomes almost 1 very quickly, so the dose-response relation then follows a virtually unmodified Beta-Binomial probability distribution for infection. Figure 2 shows that infection

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by oocysts can effectively occur with very small ingested doses of oocysts, with 1 oocyst being

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able to cause an infection with a probability of 0.46 (0.31–0.57, 95% confidence level).

Adding human exposure to the model

Human infections do not influence the definitive- and intermediate-host transmission cycle of T.

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gondii, as humans are only dead end hosts. The force of infection of oocyst-originated infections in humans is λh = βh E, with βh the rate of human infection given contact with potentially contaminated soil. This rate is directly proportional to the incidence (i = λh s, where s is

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the prevalence of susceptible humans). Therefore, by studying the reduction of λh due to cat vaccination we gain insight on the reduction of oocyst-originated human T. gondii infections. The probability of infection depends both the probability of being exposed to a certain

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dose of oocysts and on the probability of becoming infected due to ingesting said oocyst dose (oocyst dose-response relation for infection). Even when considering the lowest values of the dose-response range calculated by the Bayesian analysis in § 2.3, the probability of infection

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remains high for the ingestion of even one oocyst, so we simplified our analysis by assuming that infection will always occur after exposure. Depending on the model approach for environmental contamination (see § 2.1.3), the interpretation of βh and E are different and would have different

values. In the case of M = 1 (i.e., the approach from L´elu et al., 2010), βh is related to the probability per unit time of a human finding (and ingesting) any oocyst dose while in a contaminated patch of environment, when a fraction E of the environment is contaminated.

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These doses will in practice always be infectious because in this case oocysts are expected to be clustered in large enough numbers (a binary situation of finding/ingesting either zero or many oocysts, but not in between numbers), e.g., gardening close to where a cat has defecated. In the case of M = 0 (i.e., the approach from Turner et al., 2013), βh represents the combined probability per unit time of finding (ingesting) an infectious oocyst and becoming infected with it, while all the environment is contaminated with a total amount of oocysts proportional to E. We studied the consequences of cat vaccination under both approaches for comparison.

Results

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The results are presented as a function of vaccination coverage, where the model compartment

values are those for which the system settles at dynamic equilibrium, i.e., after some time has passed they do not change further as time keeps passing by. Fig. 3 shows the steady states

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values for all compartments in the models and are shown as absolute population size. Normally, when dealing with directly transmitted infectious diseases it is useful to show results in terms

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of population fractions, which remain the same, regardless of the total absolute population. However, in our models for T. gondii infection transmission occurs through the environment, which works as a reservoir for infection. This breaks the dependence of the force of infection

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on the cat population fractions because environmental contamination occurs according to the absolute number of cats which are shedding and have shed oocysts. Therefore, the panels in Fig. 3 show results for four different cat populations, 1000, 100, 50 and 20 cats, respectively.

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With small cat populations (50 and 20 cats), there is no substantial difference between results when comparing the two environmental infection approaches (M = 1 and M = 0), which is expected for low levels of environmental contamination E (see § 2.1.3, Eq. (1)). In the model

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assuming a population of 1000 cats, results on the number of recovered cats (R1 ) and infectious mice (I2 ) vary more notably because of the obvious difference in the values of E, as the latter scales proportional to the number of infectious cats (I1 ) when M = 0, and saturates at a value

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of 1 when M = 1. The number of infectious cats (I1 ), though, was barely increased (almost non accountable for) in the models where infectiousness is proportional to the number of oocyst (M = 0). This is explained by the assumption of predation of one mouse per week per cat, which then makes predation the main source of infection among cats in comparison to oocyst-originated cat infections. As infection depends on the absoulte number of susceptible cats available, i.e., the absolute

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Figure 3: Predicted values for each model compartment (Eq. (2)) at dynamic equilibrium, when considering the full range of vaccination coverages. Solid lines show results for models

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assuming a fixed probability of infection when on a contaminated patch of environment (M = 1, oocysts are clustered, L´elu et al., 2010). Dashed lines show results for models assuming a

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probability of infection proportional to total oocyst number (M = 0, oocysts homogeneously distributed, Turner et al., 2013). Results are considering the cat population indicated above each panel and a predation rate of one mice per week per cat.

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number of non-vaccinated cats, the needed vaccination ratio to achieve an important reduction of the disease depends on the size of the cat population (Fig. 3). One cat sheds about 107 oocysts per defecation event, translating in total to a few 108 oocysts shed during the cat’s infectious period (Cornelissen et al., 2014). Given how infectious oocysts are to mice and other intermediate hosts (see § 2.3), just a few cats are needed to keep the environment contaminated to a level where T. gondii can sustain and the disease dynamics are more similar to those of a fully environmental pathogen. This means that when considering various population sizes, instead of a classical herd immunity concept where a minimal fraction of the population needs to be

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vaccinated for achieving disease elimination, the effect of vaccination on cats is more directly

dependent on the absolute number of cats which can still become infectious (i.e., those which

remain non-vaccinated, Nnv = N1 (1 − v)). Therefore, the disease dynamics in a population of, e.g., 1000 cats with a vaccination ratio of 95% are the same as those in a 100 cat population with 50% vaccination ratio, where in both cases 50 cats remain not vaccinated.

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Elimination prospects of T. gondii infections are shown in Fig. 4, depending on the number of non-vaccinated cats (in any given population) and on the mouse predation rate. Results are

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valid for both assumptions on environmental infection (M = 1 and M = 0), given that by definition R0 is calculated in a naive population, which in our case means that E is small. The red line shows that T. gondii infections cannot be eliminated in any population where more than

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55 (55.17) cats are not vaccinated, even if there were no prey, because cats could sustain the infection by themselves (simple life cycle only). With the inclusion of transmission by ingesting infected prey, the maximum number of non-vaccinated cats allowed for controlling the disease

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decreases strongly with an increased predation rate. In the case of our examples in Fig. 3, where predation rate of one mouse per week per cat is considered, a vaccination ratio which leaves more than 8 (8.438) non-vaccinated cats is not enough to eliminate infection.

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Lower vaccination ratios than the one needed to eliminate infection may still help to reduce the incidence of human T. gondii infections to some extent. The relative (human) incidence reduction by applying cat vaccination relates closely with the relative reduction of the force of

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infection (§ 2.4), and for all practical purposes both relative reductions can be considered to be equal. Fig. 5 shows for our four example cat populations the expected relative reduction of the force of infection of oocyst-originated toxoplasmosis, as function of vaccination coverage. Depending on how environmental contamination is modelled, the relative incidence reduction varies differently. Models assuming oocysts homogeneously distributed in the environment (M = 0, Turner et al., 2013), where the probability of infection is proportional to total number of

15

Toxoplasmosis elimination depending on number of cats and predation rate.

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R0 < 1 R0c < 1 R0s < 1

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0.6

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0.4 0.2

0

25

50

75 100 125 150 No. of non-vaccinated cats

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200

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0.0

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Predation rate [mouse per week per cat]

1.0

Figure 4: Toxoplasmosis elimination prospects as a function of non-vaccinated cats. Green

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indicates where elimination by vaccination could be achieved (R0 < 0). Red indicates where no elimination is possible, even if there is no predation at all. Underneath the grey line is the area where control could be achieved if transmission was only driven by predation. R0s and R0c in

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the legend represent respectively the simple and the complex life-cycle components of the total reproduction number R0 (see § 2.2).

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0.8

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0.6

0.2

1000 cats 100 cats 50 cats 20 cats

0.0

0.2 0.4 0.6 0.8 Prop. of Cat Population vaccinated (v)

1.0

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0.0

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0.4

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Force of infection relative change

1.0

Figure 5: Expected reduction of the toxoplasmosis force of infection as function of vaccination

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coverage. Results are shown for the different cat populations indicated in the legend. Solid lines show results for models assuming a fixed probability of infection when on a contaminated patch of environment (M = 1, oocysts are clustered, L´elu et al., 2010). Dashed lines show results for

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models assuming a probability of infection proportional to total oocyst number (M = 0, oocysts homogeneously distributed, Turner et al., 2013).

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oocysts, show a linear decrease as vaccination coverage is increased from 0 to the coverage needed for achieving elimination. Models assuming oocysts are clustered (M = 1, L´elu et al., 2010), which consider a fixed probability of infection when on a contaminated patch of environment, present a less favourable scenario. They exhibit a lower reduction for the same vaccination coverage than the models with M = 0, and the larger the cat population considered the smaller the reduction for a given vaccination coverage (of course, unless elimination has already been achieved with a smaller vaccination ratio). This difference is explained by the saturated character of the force of infection in the models with M = 1, which does not depend linearly on the number

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of oocysts (and consequently linearly on the number of shedding cats) at a given time.

Our analysis was carried out using a cat population turnover driven by the known Dutch cat death rate, where the average age of a cat is 7.7 years. Using a higher death rate like the one estimated for cats from rural areas, where the average life of a cat is 20 months (1.66 yr) (Courchamp et al., 1995; L´elu et al., 2010), makes the cat population turnover also quicker.

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Fig. 6 shows the force of infection reduction as a function of vaccination ratio for cat death rates ranging between 1/7.7 yr−1 and 1/1.66 yr−1 , for various cat population sizes and assuming a

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fixed probability of infection when on a contaminated patch of environment (M = 1, oocysts are clustered, L´elu et al., 2010). A higher mortality rate allows (in dynamic equilibrium) for a larger proportion of susceptible cats that can acquire the pathogen and shed oocysts, increasing

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the force of infection when compared to a population of cats with a slower turn over. When considering models assuming a probability of infection proportional to total oocyst number (M = 0, oocysts homogeneously distributed, Turner et al., 2013), the number of oocysts is

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proportional to the number of cats that contaminate the environment, leading to the same relative reduction of the force of infection shown in Fig. 5. Note that the critical numbers of non-vaccinated cats Nnv to achieve elimination (Fig. 4) do change with a different population

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turnover, but in these examples the difference becomes negligible. From § 2.2 we see that Nnv ∝ (b1 + γ), so the population turnover b1 needs to be of the order of the infectious period duration gamma (2 weeks) in order to substantially affect the critical number of non-vaccinated

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cats. E.g., a population turnover b1 as low as 20 weeks would only have an effect of 10% variation in in the critical numbers. Depending on the chosen predation rate, the relative reduction of the force of infection is

affected as shown in Fig. 7 for models assuming a fixed probability of infection when on a contaminated patch of environment (M = 1, oocysts are clustered, L´elu et al., 2010). Lower

limits become zero at any vaccination rate for populations smaller than the limit of 55 cats for

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0.6

1000 cats 1000 cats 50 cats 20 cats

0.0 0.0

Figure 6:

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0.2

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0.4

0.2 0.4 0.6 0.8 Prop. of Cat Population vaccinated (v)

1.0

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Force of infection relative change

1.0

Range of expected reduction of the toxoplasmosis force of infection as function of

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vaccination coverage, depending on cat population turnover. For every cat population indicated in the legend, upper and lower ribbon limits correspond to a cat population turnover where cats live on average 1,66yr and 7.7yr, respectively. Results are shown for the different cat populations

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indicated in the legend. These results are for models assuming a fixed probability of infection when on a contaminated patch of environment (M = 1, oocysts are clustered, L´elu et al., 2010).

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sustaining the infection when there is no predation (e.g, Fig. 4), so for the sake of clarity in Fig. 7, results for a total population of 20 cats are not shown. For larger populations the lower limits become larger as long as the vaccination ratio allows for a certain number of unvaccinated cats to sustain transmission without predation.Results for the upper limits (extreme predation rate of 21 mice per week per cat) are relatively close to our chosen conservative baseline of 1 mouse per week per cat, especially for larger cat populations. For models assuming a probability of infection proportional to total oocyst number (M = 0, oocysts homogeneously distributed, Turner et al., 2013), the force of infection relative reduction due to vaccination remains unchanged by predation

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rate, i.e., the same as shown in Fig. 5.

Discussion and conclusion

Using a compartmental model of T. gondii infection that considers definitive- and intermediate-

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host transmission routes we assessed the prospects of elimination transmission or significantly reducing the risk of oocyst-originated human toxoplasmosis in the Netherlands by cat vaccina-

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tion. We also calculated a plausible human oocyst-originated infection dose-response relation for T. gondii, where oocysts turned out to be extremely infectious. In our model we considered a fixed fraction of the population is “born” vaccinated rather than using a traditional vaccination

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rate. Therefore, the effects of vaccination in our model represent an optimistic best case scenario where vaccination occurs before loss of maternal immunity, it is 100% effective in preventing cats from shedding oocysts, and is lifelong lasting. Even with these favourable assumptions about

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vaccination, elimination is very difficult as only a few cats left unvaccinated are enough for sustaining transmission and infection when a predation rate of one mouse per week per cat is taken into account. Changing the vaccination approach from our model to a traditional vaccination

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rate would only reduce the already slim possibilities of control we have shown in our results, because cat infections tend to occur at young age and they could be vaccinated after their oocyst shedding episode. This means that in large (and open) populations such as stray cats, it is

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unfeasible to attain the large vaccination coverage needed for eliminating infection. However, in smaller closed populations, such as farms, vaccination can be effective in strongly reducing the force of infection on all animals (intermediate and dead-end hosts) in the farm. This could be used as a bio-security measure given that the meat products from that farm will also have a reduced probability of being contaminated, even at the very likely event of re-introduction of the pathogen (e.g., external prey, contaminated meat from other farms) in case elimination within

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1000 cats 1000 cats 50 cats

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0.6 0.4 0.2

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Force of infection relative change

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0.2 0.4 0.6 0.8 Prop. of Cat Population vaccinated (v)

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0.0

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0.0

Figure 7: Range of expected reduction of the toxoplasmosis force of infection as function of vaccination coverage, according to various predation rates. Results were calculated provided

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that the prey population is large enough to sustain the needed predation rate. For every cat population indicated in the legend, solid lines represent a predation rate of 1 prey per week,

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while upper and lower ribbon limits correspond to 21 and 0 prey per week, respectively. These results are for models assuming a fixed probability of infection when on a contaminated patch of environment (M = 1, oocysts are clustered, L´elu et al., 2010).

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the cat population has been achieved. This bio-security measure assumes that the vaccination ratio is maintained to prevent proliferation of the pathogen after a re-introduction. One could consider implementing cat vaccination in a given area or region, were many neighbouring farms are included and may be better described by meta population models. But while sort of contact structure is not well described by our simplistic model which considers only one big area where all cats are indistinctly connected, using our model can serve as guideline for individual farms, each of which containing smaller cat populations and being open to sporadic re-introductions from prey or cat contact from other farms. Note that when considering small

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cat populations, such as individual farms, stochastic effects become strong. These cannot be

properly described by our continuous deterministic model, but they effectively can have two effects. Either could get rid of the infection more effectively that in a deterministic model due to stochastic extinction, rendering vaccination more effective, or could generate transitory

outbursts of infection after which the system would achieve equilibrium as predicted by our

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model.

Partial control is possible though. Depending on the assumption on how the force of infection

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from the environment scales, the incidence of oocyst-originated human toxoplasmosis can be reduced to some extent. We considered two extreme ways of modelling the force of infection: a) proportional to the number of oocysts (M = 0, Turner et al., 2013), which represents a

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situation where oocysts are homogeneously distributed across the whole environment. b) fixed force of infection when on a contaminated patch of environment (M = 1, L´elu et al., 2010), which represents oocysts being clustered in large numbers (therefore, always an infectious

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dose) in the contaminated parts of the environment, so the force of infection represents the chance of crossing paths with environment (strongly) contaminated by cats. Considering the case when oocysts are homogeneously distributed in the environment (M =

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0, Turner et al., 2013) is the most favourable scenario, where the expected human incidence scales down almost in the same amount as the proportion of non-vaccinated cats when considering a large cat population. But considering a scenario which represents oocysts being clustered (M =

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1, L´elu et al., 2010) brings a least favourable scenario where, for large cat populations, only high cat vaccination ratios would achieve a substantial reduction of expected oocyst-originated human T. gondii infections. The real mechanism on how the T. gondii force of infection works should lay in between

the two approaches described above. But because of the high infectivity that oocysts show for various mammals and the large amount that one infected cat can shed, we favour the approach

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considering clustered oocysts in contaminated patches as the one which closer follows what in reality occurs. Kortbeek et al. (2009) estimated the yearly incidence of congenital toxoplasmosis in the Netherlands to be 0.2%, providing an upper limit to oocyst acquired toxoplasmosis incidence, as women are expected to follow general pregnancy health advise, avoiding consumption of undercooked meats. The rate of toxoplasmosis infections per year is relatively small compared to the number of oocysts that one infectious cat sheds (about 107 oocysts per defecating event and more than 108 during their infectious period Cornelissen et al., 2014). Combining these numbers and the fact that oocysts are long lasting and highly infectious each, it suggests that

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human infections follow more of an all-or-nothing exposure-infection mechanism. This would

favour the model as proposed by L´elu et al. (2010), where the probability of infection is related to whether exposure to contaminated environment occurs, rather than the model by Turner et al. (2013), where infection depends on the degree of contamination (number of oocysts) in the

environment. For example, if oocysts from faeces were to be diluted and homogeneously spread

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across the European Dutch soil (33893km2 ), about 100 shedding cats in the whole country would be enough to have one highly infectious oocyst per square meter.

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In our study we used the average life expectancy of cats in the Netherlands as death rate. This rate is the one regulating the cat population turnover, and not the (faster) cat birth rate as used in other studies (e.g., L´elu et al., 2010; Turner et al., 2013). Thus, cats have a

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lower mortality rate and their population is renewed at a slower rate than in previous studies, making our study somewhat optimistic from the point of view of vaccination ratios needed for controlling toxoplasmosis. A shorter cat lifespan increases the cat population turnover and with

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it the availability of susceptible cats at a given time point, increasing the vaccination coverage needed for achieving the same reduction of T. gondii infections when compared to slower cat population turnover rates (Fig. 6). By following the example of other studies where basically

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the cat birth rate drives the population turnover (e.g., L´elu et al., 2010; Turner et al., 2013, used one cat born every 5 months), the vaccination coverage needed to achieve a given reduction in the force of infection would be yet higher than those we show in Fig. 6.

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The cats to mice population ratio used was high enough to make sure that all cats can find a

prey at the assumed predation rate. An increase in the mouse population would have no effect as cats are able to find enough prey for the assumed predation rates. A decrease of the mouse population would only have an effect if the mice population is reduced enough to prevent cats from hunting at the assumed predation rate, slowing the predation and consequently reducing transmission of T. gondii via the complex life-cycle, which includes the intermediate host. A

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similar effect as decreasing the mouse population can result from keeping the mouse population fixed and increasing the predation rate to extreme values such that that prey are caught too often to replenish and even too quick to have time to become infected, lowering further the prevalence in cats. However, this can occur only at unrealistically large predation rates. Fig. 7 shows that even when considering a rate of 3 prey per day (upper ribbon limits), the force of infection is not very different from that when only one prey per week is considered, for any given vaccination ratio. Our calculation of oocyst-originated infectious dose-response relation for humans was based

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only on data collected for other intermediate and dead end mammalian hosts because there is no data available for humans. Even when considering the lowest values for the oocyst doseresponse for infection obtained with the Markov-chain calculations, oocysts turn out to be so

extremely infectious for intermediate hosts (but not for cats) that we considered they always cause infection. A dose-response relation providing lower probabilities of infection for a given

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dose would make vaccination more effective for preventing oocyst-originated toxoplasmosis, but

only when considering the models assuming a probability of infection proportional to total

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oocyst number (M = 0, oocysts homogeneously distributed, Turner et al., 2013). For example, Guo et al. (2016) scaled up the mouse and rat dose-response to fit the congenital bradyzoiteoriginated disease attribution ratio 22% from questionnaires. A similar approach could be used

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for obtaining an estimation of the oocyst dose-response relation, however, this would place the whole chain of events of encountering the oocysts and becoming infected with them as a pure dose response effect. For models that assume of a fixed probability of infection when on a

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contaminated patch of environment (M = 1, oocysts are clustered, L´elu et al., 2010), the fact that one infectious cat can shed about 107 oocysts per defecation event suggests that only an unrealistic extreme change in the dose-response relation would be needed to affect our current

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findings.

Prospects on preventing oocyst-originated human toxoplasmosis by vaccination in large populations of cats are not favourable due to the large vaccination coverage needed. However, in

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this study we did not consider the consequences of reduction of infected livestock and meatborne toxoplasmosis cases. Within the context of a meat producing farm with live stock, it may turn out that cat vaccination in farms has an important effect because it can be assumed that the reduction of oocyst-originated infections on other intermediate hosts is comparable to that calculated for humans. Consequently, reducing oocyst-originated infection locally within a meat producing farm would reduce the risk of that farm producing contaminated products, and in

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turn, its contribution as a source to meatborne human T. gondii infections. In conclusion, we showed using two different models that vaccination of cats might only be effective if applied in small cat populations such as present in farms. In large cat populations, the feasibility of cat vaccination is almost impossible because of the high vaccination coverage needed.

Acknowledgements

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The authors would like to acknowledge T. L. Feenstra, M. Lambooij, M. J. J. Mangen, E. A. B. Over, J. J. Polder and G. A. de Wit, for their input and participation in the ToxoScan project, financed by the Dutch National Institute for Public Health and Environment (RIVM), under which this study was made possible.

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