In this paper, we investigate a nonautonomous and an autonomous model of schistosomiasis transmission with a general incidence function. Firstly, we formulate the nonautonomous model by taking into account the effect of climate change on the transmission. Through rigorous analysis via theories and methods of dynamical systems, we show that the nonautonomous model has a globally asymptotically stable disease-free periodic equilibrium when the associated basic reproduction ratio [Formula: see text] is less than unity. Otherwise, the system admits at least one positive periodic solutions if [Formula: see text] is greater than unity. Secondly, using the average of periodic functions, we further derive the autonomous model associated with the nonautonomous model. Therefore, we show that the disease-free equilibrium of the autonomous model is locally and globally asymptotically stable when the associated reproduction ratio [Formula: see text] is less than unity. When [Formula: see text] is greater than unity, the existence and global asymptotic stability of the endemic equilibrium is established under certain conditions. Finally, using linear and nonlinear specific incidence function, we perform some numerical simulations to illustrate our theoretical results.

中文翻译：

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具有一般发病函数的血吸虫病传播季节数学模型的全球动态

在本文中，我们研究了具有一般发病率函数的非自治和自治血吸虫病传播模型。首先，我们通过考虑气候变化对传输的影响来制定非自治模型。通过对动力系统的理论和方法的严格分析，我们表明当相关的基本繁殖率[公式：见正文]小于一时，非自治模型具有全局渐近稳定的无病周期平衡。否则，如果 [公式：见正文] 大于一，则系统承认至少一个正周期解。其次，利用周期函数的平均值，我们进一步推导出与非自治模型相关的自治模型。所以，我们表明，当相关的繁殖率 [公式：见文本] 小于 1 时，自主模型的无病平衡是局部和全局渐近稳定的。当[公式：见正文]大于一时，在一定条件下，地方性平衡的存在性和全局渐近稳定性成立。最后，使用线性和非线性特定入射函数，我们进行了一些数值模拟来说明我们的理论结果。