In this paper, we proposed and analyzed a nonlinear deterministic model for the impact of temperature variability on the epidemics of the malaria. The model analysis showed that all solutions of the systems are positive and bounded with initial conditions in a certain set. Thus, the model is proved to be both epidemiologically meaningful and mathematically well-posed. Using the next-generation matrix approach, the basic reproduction number with respect to the disease-free equilibrium (DFE) point is obtained. The local stability of the equilibria points is shown using the Routh–Hurwitz criterion. The global stability of the equilibria points is performed using the Lyapunov function. Also, we proved that if the basic reproduction number is less than one, the DFE is locally and globally asymptotically stable. But, if the basic reproduction number is greater than one, the unique endemic equilibrium exists, locally and globally asymptotically stable. The sensitivity analysis of the parameters is also described. Moreover, we used the method implemented by the center manifold theorem to identify that the model exhibits forward and backward bifurcations. From our analytical results, we confirmed that the variation of temperature plays a significant role on the transmission of malaria. Lastly, numerical simulations are demonstrated to enhance the analytical results of the model.

中文翻译：

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温度变化对 SIRS 疟疾模型的影响

在本文中，我们提出并分析了温度变化对疟疾流行的影响的非线性确定性模型。模型分析表明，系统的所有解都是正解，并且在一定集合中以初始条件为界。因此，该模型被证明具有流行病学意义和数学适定性。使用下一代矩阵方法，获得关于无病平衡 (DFE) 点的基本再生数。使用 Routh-Hurwitz 准则显示平衡点的局部稳定性。使用 Lyapunov 函数执行平衡点的全局稳定性。此外，我们证明了如果基本再生数小于 1，则 DFE 是局部和全局渐近稳定的。但，如果基本繁殖数大于 1，则存在独特的地方性平衡，局部和全局渐近稳定。还描述了参数的敏感性分析。此外，我们使用中心流形定理实现的方法来识别模型表现出前向和后向分叉。根据我们的分析结果，我们证实温度的变化对疟疾的传播起着重要作用。最后，数值模拟被证明可以增强模型的分析结果。我们使用中心流形定理实现的方法来识别模型表现出前向和后向分叉。根据我们的分析结果，我们证实温度的变化对疟疾的传播起着重要作用。最后，数值模拟被证明可以增强模型的分析结果。我们使用中心流形定理实现的方法来识别模型表现出前向和后向分叉。根据我们的分析结果，我们证实温度的变化对疟疾的传播起着重要作用。最后，数值模拟被证明可以增强模型的分析结果。