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

TL;DR

This study develops a mathematical model to analyze rabies transmission dynamics among humans and dogs, highlighting the critical role of contact rates and environmental factors, and suggesting control strategies focused on dog population management.

Contribution

The paper introduces a novel mathematical model incorporating contact and environmental factors to assess rabies spread, including sensitivity analysis and the impact of periodic transmission variations.

Findings

Reproduction number $\\mathcal{R}_{0}$ determines stability of disease states.

Contact rates significantly influence rabies transmission.

Reducing dog populations can effectively control rabies spread.

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, $\mathcal{R}_{0}$, using the next generation matrix method. When $\mathcal{R}_{0}<1$, the disease-free equilibrium is globally stable, whereas when $\mathcal{R}_{0}>1$, the endemic equilibrium is globally stable. To identify the most influential parameters in disease transmission, we used the normalized forward sensitivity index. Our 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. Therefore, the study proposes that to mitigate the factors most strongly linked to disease sensitivity, effective disease control measures should primarily prioritize on reducing the population of both free-range and domestic dogs in open environments.