Impact of Quiescence on the Final Size Distribution of SIQR Epidemic Model using Selke Construction

Abstract

Mathematical modelling is used to understand the spread of infectious diseases such as malaria, covid-19, HIV etc. in this research, we consider Selke construction which is probabilistic approach to study the fine size distribution of an epidemic. We added quiescence phase to the standard susceptible – infected – recovered (SIR) model and build susceptible – infected – quiescence – recovered (SIQR) model to examine the effect of quiescence. We find out that quiescence phase does not affect the basic reproduction number  as well as the final size distribution. However, it does affect the timing, the peak and the duration of the epidemics. We also perform Sensitivity analysis on the parameters of the models.

Keywords: Selke Construction, Sensitivity Analysis, Quiescence Phase, Basic Reproduction Number, Final Size Distribution.