Mathematical model to assess the impact of contact rate and environment factor on transmission dynamics of rabies in humans and dogs

Abstract

This paper presents a mathematical model to understand how rabies spreads among humans, free-range, and domestic dogs. By analyzing the model, we discovered that there are equilibrium points representing both disease-free and endemic states. We calculated the basic reproduction number, $R_0$ using the next generation matrix method. When $R_0<1$ , the disease-free equilibrium is globally stable, whereas when $R_0\ge 1$ , the endemic equilibrium is globally stable. To identify the most influential parameters in disease transmission, we used the normalized forward sensitivity index. The simulations revealed that the contact rates between the infectious agent and humans, free-range dogs, and domestic dogs, have the most significant impact on rabies transmission. The study also examines how periodic changes in transmission rates affect the disease dynamics, emphasizing the importance of transmission frequency and amplitude on the patterns observed in rabies spread. To reduce disease sensitivity, one should prioritize effective disease control measures that focus on keeping both free-range and domestic dogs indoors. This is a crucial factor in preventing the spread of disease and should be implemented as a primary disease control measure.

Keywords: Contact rate; Environment; Mathematical model; Periodic transmission; Rabies disease.