Abstract We develop a periodic compartmental population model for the spread of malaria, dividing the human population into two classes: non-immune and semi-immune. The effect of seasonal changes in weather on the malaria transmission is considered by applying a non-autonomous model where mosquito birth, death and biting rates are time-dependent. We show that the global dynamics of the system is determined by the basic reproduction number, which we define as the spectral radius of a linear integral operator. For values of the basic reproduction number less than unity, the disease-free periodic solution is globally asymptotically stable, while if R 0 > 1 , then the disease remains endemic in the population. We show simulations in accordance with the analytic results. Finally, we show that the time-average reproduction rate gives an underestimation for malaria transmission risk.

中文翻译：

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阈值和稳定性导致具有人类部分免疫的疟疾传播的周期性模型

摘要 我们为疟疾的传播开发了一个周期性的区室人口模型，将人口分为两类：非免疫性和半免疫性。天气的季节性变化对疟疾传播的影响是通过应用非自主模型来考虑的，其中蚊子的出生、死亡和叮咬率与时间有关。我们表明系统的全局动力学由基本再现数决定，我们将其定义为线性积分算子的谱半径。对于小于 1 的基本再生数的值，无病周期解是全局渐近稳定的，而如果 R 0 > 1，则该疾病在人群中保持地方性。我们根据分析结果显示模拟。最后，