Mathematical study for an infectious disease with awareness-based SIS-M model

Abstract

In this article, we discuss a mathematical model of Susceptible-Infected-Susceptible-Media (SIS-M), which considers the level of human awareness on certain presence of disease. To construct the model, we divided the population based on their health status into susceptible individuals unaware and aware of the disease and the infectious individuals. The level of awareness included private awareness associated with direct contacts between unaware and aware populations, global awareness due to reported cases of infection, and regular awareness campaigns from media or policy makers. The dynamical behaviour of the model was analysed rigorously. The disease-free equilibrium point, the endemic equilibrium point, and the basic reproduction number were shown in this model analytically and numerically. We found that the disease-free equilibrium point was locally asymptotically stable if R 0 < 1, and unstable if R 0 > 1. From the sensitivity analysis of R 0, it was found that there was a minimum intensity for the awareness campaign so that the level of awareness manifested in the efforts of individuals to protect themselves from disease successfully eradicate the disease from the community. This result indicates that the efforts of individuals in protecting themselves can have a massive effect on the existence of the disease in the community.