An infectious disease epidemic model with migration and stochastic transmission in deterministic and stochastic environments

Abstract

Understanding population migration is essential for controlling highly infectious diseases. This paper studies the global dynamics of an infectious disease epidemic model incorporating population migration and a stochastic transmission rate. Our findings demonstrate that in deterministic and stochastic environments, the models exhibit global Lyapunov stability near the disease-free equilibrium point, determined by a threshold parameter. Furthermore, we analyze the effect of migration on infectious diseases. We discover that the number of infections and the peak value of the infection curve increase with a higher level of population migration. These results are supported by numerical illustrations that hold epidemiological relevance. Additionally, the disease-free equilibrium of the associated time delay model is linearly asymptotically stable, and the endemic equilibrium exhibits more bifurcation for larger time delay values.

Keywords

• Epidemic model
• Stochastic stability
• Basic reproduction number
• Lyapunov stability
• Wiener process