School of Mathematics and Information Science, Guangzhou University, Guangzhou, People's Republic of China.
Department of Mathematics, Luliang University, Luliang, People's Republic of China.
J Biol Dyn. 2020 Dec;14(1):368-388. doi: 10.1080/17513758.2020.1771443.
This paper proposes a malaria transmission model to describe the dynamics of malaria transmission in the human and mosquito populations. This model emphasizes the impact of limited resource on malaria transmission. We derive a formula for the basic reproductive number of infection and investigate the existence of endemic equilibria. It is shown that this model may undergo backward bifurcation, where the locally stable disease-free equilibrium co-exists with an endemic equilibrium. Furthermore, we determine conditions under which the disease-free equilibrium of the model is globally asymptotically stable. The global stability of the endemic equilibrium is also studied when the basic reproductive number is greater than one. Finally, numerical simulations to illustrate our findings and brief discussions are provided.
本文提出了一个疟疾传播模型，用于描述人类和蚊子群体中疟疾传播的动态。该模型强调了有限资源对疟疾传播的影响。我们推导出了感染的基本繁殖数的公式，并研究了地方病平衡点的存在性。结果表明，该模型可能发生逆向分歧，其中局部稳定的无病平衡点与地方病平衡点共存。此外，我们确定了模型无病平衡点全局渐近稳定的条件。当基本繁殖数大于 1 时，还研究了地方病平衡点的全局稳定性。最后，通过数值模拟来说明我们的发现，并进行了简要的讨论。
