ABSTRACT

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.

摘要

本文提出了一种疟疾传播模型来描述人类和蚊子种群中疟疾传播的动态。该模型强调了有限资源对疟疾传播的影响。我们推导了感染的基本生殖数量的公式，并研究了地方性均衡的存在。结果表明，该模型可能会发生反向分叉，局部稳定的无病平衡与地方平衡共存。此外，我们确定模型的无病平衡在全局渐近稳定下的条件。当基本生殖数大于1时，还研究了地方均衡的全局稳定性。最后，提供了数值模拟来说明我们的发现并进行了简短的讨论。