A mathematical model incorporating exogenous reinfection and primary progression infection processes is proposed. Global stability is examined using the geometric approach which involves the generalization of Poincare-Bendixson criterion for systems of -ordinary differential equations. Analytical results show that for a Susceptible-Exposed-Infective-Recovered (SEIR) model incorporating exogenous reinfection and primary progression infection mechanisms, an additional condition is required to fulfill the Bendixson criterion for global stability. That is, the model is globally asymptotically stable whenever a parameter accounting for exogenous reinfection is less than the ratio of background mortality to effective contact rate. Numerical simulations are also presented to support theoretical findings.

中文翻译：

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包含外源性再感染和原发感染机制的 SEIR 模型的全局稳定性条件

提出了一种包含外源性再感染和原发性进展感染过程的数学模型。全局稳定性是使用涉及庞加莱-环域标准的用于系统的概括的几何方法检查-常微分方程。分析结果表明，对于包含外源性再感染和原发性进展感染机制的易感暴露感染恢复 (SEIR) 模型，需要一个额外的条件来满足全球稳定性的 Bendixson 标准。也就是说，当考虑外源性再感染的参数小于背景死亡率与有效接触率的比率时，该模型全局渐近稳定。还提供了数值模拟以支持理论发现。