Modeling Epidemics: A Primer and Numerus Software Implementation

Wayne M. Getz; Richard Salter; Oliver Muellerklein; Hyun S. Yoon; Krti Tallam

In the context of an epidemic occurring in a single homogeneous population of size N at the start of the epidemic (i.e., at time t = 0), denote the per-capita susceptible (S) disease transmission rate by τ (I, N ), which we assume depends on both the number of infectious individuals I(t) and the total number of individuals N (t) in the population. In addition, we denote rates of progression from exposed (E) to infectious (I) and onto to removed with immunity (V ) using the symbols σ and γ respectively (Figure 1 ). For generality, as depicted in Figure 1A , we include a population net recruitment function λ(t), where all these recruits are assumed to be susceptible. Later we generalize this in the context of a metapopulation structure and allow other disease classes to migrate. We also include per capita disease-induced and natural mortality rates α and µ, respectively, that accumulate in disease class D, as well as allow for the occurrence of a per capita immunity-waning rate ν ( Figure 1 ). Some or all of this latter group of parameters may be zero, and only become nonzero as the scope of the analysis undertaken is enlarged. Also, as a starting point, all parameters are assumed to be constant, except for the transmission function τ , which at its most fundamental has the relatively simple "frequency-All rights reserved. No reuse allowed without permission.