Qualitative behavior of SIS epidemic model on time scales

Abstract

Mathematical models in continuous or discrete time are widely used to simplify real-world systems in order to understand their mechanisms for a particular purpose. Consequently, a welldefined model should be able to carry out some predictions and be fitted to observational data in a variety of time measurements (seconds, hours, days, weeks, months, or years). Therefore, the time scales approach also plays an important role in the model. In this paper, we construct a time scales version of a simple epidemic model (SIS) and explore the variety of its qualitative behavior. For each parameter value, the theory of time scales allows the discovery of similar and dissimilar behavior of SIS epidemic models on different time scales. Finally, the dynamic behavior shows a period doubling bifurcation path to chaos as the distance of equally spaced points in time increases.