A Combined Study of Autonomous and Nonautonomous Systems for Zoonotic Diseases

Abstract

Zoonotic diseases transmitted naturally between humans and animals pose a major and persistent threat to global health security. Recent outbreaks such as avian influenza, Ebola, SARS, and COVID-19 have highlighted the complexity of pathogen transmission across species and the urgent need for integrated approaches to understand their dynamics. Despite significant progress in infectious disease modeling, many existing models fail to capture the full transmission pathways connecting wild, domestic, and human populations, as well as the effects of pathogen mutation. This study develops and analyzes both autonomous and nonautonomous mathematical models for a zoonotic disease system that explicitly incorporate interactions among wild, domestic, and human populations. Using analytical and numerical techniques, we investigate the stability of steady states and analyze the impact of transmission rates both within and between populations on infection dynamics in the compartments to understand the overall burden of disease in humans. In addition, we consider the role of mutation rates in shaping the course of the epidemic, particularly in the context of cross-species transmission. The model is implemented numerically in Python using the finite difference technique to simulate transient and steady-state behaviors under varying transmission scenarios. Results reveal that the disease may persist endemically within all populations when cross-species transmission and mutation rates exceed threshold values, or it may die out in the animal populations but persist in humans underscoring the importance of intermediate hosts in sustaining infection. The findings improve the quantitative understanding of zoonotic disease evolution and persistence under dynamic conditions, providing a theoretical basis for designing more effective control and prevention strategies targeting both human and animal reservoirs.