# Table 1 Definitions and values of the main variables, functions and parameters in the model

Process Definition Value Ref.
Number of X patches 230
Number of Y patches 230
Environment
Diffusion Percentage of contamination diffusing to the 8 neighboring patches 10%
Decay Decontamination rate 1/125 day−1 
Rodents
Birth Birth rate (b m ) 10/365 day −1 Value in the range of  and 
Density dependent probability of birth of 1 juvenile by an adult rodent b m – 0.5(b m m m ) × N m,i /K m,i
Mortality Mortality rate (m m ) 2/365 
Density dependent probability of rodent mortality m m  + 0.5(b m m m ) × N m,i /K m,i
Density Nm,i = number of mice in the 46 × 46 patches (=460 × 460 m2) subdivision i
K m,i = local carrying capacity of rodents (=Initial number of rodents) in the 46 × 46 patches subdivision i 300 *
Maturation Weaning age of rodents 21 days 
Age at sexual maturation of rodents 50 days 
Movement Range of patches travelled (in any direction) randomly chosen 0-2 patches 
Infection Probability of vertical transmission 0.15 Value in the range of  and 
Probability of rodent infection after ingesting one oocyst 1 
Number of contact between rodent and the patch/day 12 *
Probability of infection from the environment while on patch j 1-(1-p conta, j )12 See above
p conta, j  = level of contamination of patch j
Cats
Birth Birth rate (b c ) 2.4/365 day −1 
Density dependent probability of birth of 1 juvenile by an adult cat b c – 0.5(b c m c ) × N c /K c
Mortality Mortality rate (m c ) 0.6/365 day−1 
Density dependent probability of cat mortality m c  + 0.5(b c m c ) × N c /K c
Density N c  = total number of cat on the entire site area
Carrying capacity of cats (=Initial number of cats) 100 order of magnitude observed in the field 
Maturation Weaning age of cats 50 days 
Age at sexual maturation of cats 240 days 
Movement Random cat location per activity within their homerange   Estimated from maximum distance from [29, 30]
Cat homerange radius picked in a gamma distribution Γ(2, 0.014)
Infection Probability of predation of rodent within 1 patch (=10 m) of a cat 1 *
Probability of cat infection after eating an infected rodent 1 
Probability of cat infection after ingesting one oocyst 10−3 
Probability of infection from the environment while on patch j 10−3 × p conta,j see above
Prepatent period before oocyst shedding 7 days 
Duration of infectiousness (=oocyst shedding period) 14 days 
Environmental contamination Probability of cat shedding oocysts per day 1 
Level of contamination on a patch j after shedding of oocyst by one infected cat 0.01 + p conta,j See text
1. * chosen to obtain realistic values of rodent predation, rodent prevalence.