Two Populations but a One-Mitigation Policy: A β(·)-SIR Approach

In the case of a high-risk infectious disease affecting two distinct (without demographic interactions) human populations, e.g., differentiated by their settlement areas, we assume the implementation of a health non-pharmaceutical mitigation policy. However, this policy is based solely on indicators from one of the populations. Using a mathematical model that integrates β(·)-SIR representations—where β(·) is a variable specific to each population and is governed by a dynamic law (a differential equation coupled to state variables)—the dynamic consequences of the epidemiological processes in both populations are explored and compared analytically and numerically. Mainly, it studies the role of the so-called reaction (intensity of the mitigation) and restitution factor (human compliance).