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 | [31] |
Rodents | |||
Birth | Birth rate (b m ) | 10/365 day −1 | |
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 | [32] |
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 | [27] |
Age at sexual maturation of rodents | 50 days | [27] | |
Movement | Range of patches travelled (in any direction) randomly chosen | 0-2 patches | [33] |
Infection | Probability of vertical transmission | 0.15 | |
Probability of rodent infection after ingesting one oocyst | 1 | [34] | |
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 | [32] |
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 | [32] |
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 [19] | |
Maturation | Weaning age of cats | 50 days | [27] |
Age at sexual maturation of cats | 240 days | [27] | |
Movement | Random cat location per activity within their homerange | ||
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 | [34] | |
Probability of cat infection after ingesting one oocyst | 10−3 | [34] | |
Probability of infection from the environment while on patch j | 10−3 × p conta,j | see above | |
Prepatent period before oocyst shedding | 7 days | [10] | |
Duration of infectiousness (=oocyst shedding period) | 14 days | [10] | |
Environmental contamination | Probability of cat shedding oocysts per day | 1 | [35] |
Level of contamination on a patch j after shedding of oocyst by one infected cat | 0.01 + p conta,j | See text | |