Modeling Epidemics: A Primer and Numerus Software Implementation

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

The assumption that the transmission rate per susceptible individual is a relatively simple function of host population and infectious class densities (or numbers). For example, Equation 1 assumes that total transmission has a frequency dependent form. A more general case that assumes transmission is essentially i) density dependent when population density N is small relative to some function-location parameter L, and ii) frequency dependent when the population is much larger than L, takes the form τ (I, N ) = βI N + L More complicated functions have been proposed [12, 21] , including a negative binomial expression that accounts for susceptible host aggregation [38] or the phenomenon of superspreaders [39] , however, they are also limited in adhering to the following assumption. 4 . The assumption that the system is memoryless. This assumption implies that formula-All rights reserved. No reuse allowed without permission.