Table 1 Variables and parameters of the environmentally mediated infectious disease models
Variables | |
S(t) | Number of susceptible people |
I(t) | Number of infectious people |
R(t) | Number of recovered people |
W(t) | Concentration of pathogens in the environment |
W1(t) | Concentration of labile pathogens in the environment |
W2(t) | Concentration of persistent pathogens in the environment |
Parameters | |
γ | Recovery rate (per day) |
α | Deposition rate of pathogens per unit volume of environment (per day) |
η | Fraction of deposited pathogens that are labile |
δ i | Rate at which pathogen of phenotype i convert to the other phenotype (per day) |
π i | Per-pathogen probability of infection for phenotype i |
μ i | Pathogen decay rate for phenotype i (per day) |
κ | Rate at which individuals contact the environment (per day) |
N | Population size |
ρ | Volume of environment consumed (per contact) |
V | Total volume of the environment |
ξ i | Overall pathogen removal rate for phenotype i (per day), μi+κρN/V |
τ i | Average persistence of pathogen phenotype i (days) |
ϕ i | Probability that conversion from phenotype i occurs before decay |