Influence of Quiescence on the Final Size Distribution of SIQR Model

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 a probabilistic approach used to study the final 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 on the final size distribution of an epidemic. We find out analytically and by using simulation that the quiescence phase does not affect the basic reproduction number  as well as the final size distribution of the epidemic. However, it does affect the timing, the peak and the duration of the epidemic. We use next generation matrix in computing the basic reproduction number . We also perform sensitivity analysis on the parameters of the models using MATLABR2019a. We find that when the rate of entering quiescence stage (σ) increases while the rate of exiting the quiescence ( remains constant, then the peak of the disease curve decreases and the time until the epidemic ends increases. We also find that when keeping the rate of entering quiescence stage (σ) fixed and increase the rate of exiting the quiescence state (, then the peak of the disease curve increases while the time until the epidemic ends decreases.