Transmission dynamics of a two-strain pairwise model with infection age

Abstract

• A two-strain pairwise epidemic model with non-Markovian recovery process is established. • A hyperbolic system can be transformed into an integral differential system by using the method of characteristic. • We carry out rigorous analysis and obtain the relationship between the reproduction number and the final epidemic size. • Three commonly used recovery time distributions on the reproduction number were compared by numerical simulations. • The mean length of the infectious period affects the final epidemic size, the peak time, and the duration of an epidemic. We present and study a two-strain pairwise epidemic model with non-Markovian recovery process in which the recovery rate depends on infection age. The novel model is a hyperbolic system which can be transformed into a system of integro-differential equations by using the method of characteristics . For the two-strain pairwise model, the reproduction number with arbitrary recovery time distributions is obtained. We carry out rigorous analysis and obtain upper and lower estimates for the final epidemic size. Finally, the effects of three commonly used recovery time distributions on the reproduction number are compared by numerical simulations. We further present how the mean length of the infectious period affects the final epidemic size, the peak time and the duration of an epidemic.