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.
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