Modeling Infectious Diseases via Integral Delay Equations

Abstract

Integral delay equations (IDE) have several applications, they can be found in mathematical models of population and propagation of infectious diseases. Many of these models are sets of non-linear integral delay equations similar to the classical SEIR models, but with the advantage of simplifying the number of equations with a simple change of variable. An alternative equation is the well known renewal equation which can model both demographics and infectious diseases, we focus on the disease model and establish the equivalence between the versions with a single finite delay and the one with multiple delays, both obtained from a histogram of relative frequencies of tracking data of the infected people. We compare their Lyapunov matrices and the stability analysis when the reproductive number is in matrix form.