A compartmental model with a time-varying contact rate, the seasonality effect, and its corresponding nonautonomous model are investigated. The model is developed based on the six compartments: susceptible, latent, infected, asymptomatic, treated, and recovered individuals. We determine the effective reproduction number for this nonautonomous system, and analytic discussion shows that at least one positive periodic solution exists for ${\mathcal{R}}_0>1$. The model is simulated using the RK-45 numerical method, and the parameter values for the model are taken from the available literature. From the numerical results, we observe that the degree of seasonality and vaccine efficacy significantly impact the amplitude of the epidemic curve. The latent-infected phase plane shows that periodic solutions exhibit a period-doubling bifurcation as the amplitude of seasonality increases. Finally, the model outcome was compared with the actual field data and found to be consistent.

研究了具有时变接触率的分区模型、季节性效应及其相应的非自治模型。该模型是根据六个部分开发的：易感者、潜伏者、感染者、无症状者、治疗者和康复者。我们确定了这个非自治系统的有效再生数，分析讨论表明至少存在一个正周期解${\mathcal{右}}_0>1$。该模型使用 RK-45 数值方法进行模拟，模型的参数值取自现有文献。从数值结果来看，我们观察到季节性程度和疫苗功效显着影响流行曲线的幅度。潜伏感染相平面表明，随着季节性幅度的增加，周期解表现出倍周期分岔。最后，将模型结果与现场实际数据进行比较，发现模型结果是一致的。