Analyzing the Dynamics of a periodic SIQR epidemic model with mild and severe infectious

Based on the seasonal characteristics of infectious diseases, we present a non-autonomous compartmental model that considers mild and severe infection populations. We adopt different isolation methods for these two infected populations. The transmission period is divided into off-season and peak season . This study aims to provide the theoretical basis for controlling such infectious diseases. First, we use the Lipschitz condition to prove the model has a unique solution. Then, we construct a periodic linear system and obtain its fundamental solution matrix . The basic reproduction number is given by the equation . Furthermore, the disease-free equilibrium is globally asymptotically stable if . In addition, sensitivity analysis shows that if there are more mild infections within a period, then the infection rate ( ) and home isolation rate have a significant impact on . If the proportion of peak season is high, then we have . It indicates that reducing the infection rate can effectively control the spread of the epidemic compared with reducing . In summary, we can determine the most effective way to control the disease based on the number of mild and severe patients and the proportion of off-season and peak-season. Finally, we select two sets of parameters for numerical simulation.