Mathematical models for infectious diseases are considered. The exact solutions of SIR model are analyzed in terms of oscillatory motion in susceptible–infected (S–I) phase space. SIR model can not apply the effect of repeated epidemics, and then, we introduce inflow population into SIR model and name it SIR-i model. Stability is analyzed around a stable equilibrium point in S–I phase space. The nature of the phenomenon is governed by (contact rate) × (inflow population)/(removal rate) and (removal rate). Numerical examples are shown and discussed with parameters of COVID-19.

中文翻译：

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流行病模型的数学分析及其在COVID-19中的应用

考虑了传染病的数学模型。SIR模型的精确解根据易感感染（S – I）相空间中的振荡运动进行分析。SIR模型不能应用重复流行病的影响，因此，我们将流入人口引入SIR模型并命名为SIR-i模型。在S – I相空间的稳定平衡点附近分析稳定性。现象的性质由（接触率）×（流入人口）/（清除率）和（清除率）决定。数值示例显示并与COVID-19的参数进行了讨论。