Bifurcation analysis of a mathematical model for malaria transmission
Bifurcation analysis of a mathematical model for malaria transmission
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DOI：
10.1137/050638941
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发表时间：
2006-01-01
影响因子：
1.9
通讯作者：
Hyman, J. M.
中科院分区：
文献类型：
--
作者：
Chitnis, Nakul;Cushing, J. M.;Hyman, J. M.
我们提出了疟疾在人类和蚊子种群中传播的常微分方程数学模型。易感人群被传染性蚊子叮咬后也会被感染。然后，在重新进入易感类之前，他们通过暴露类、感染类和恢复类。易感蚊子在叮咬有传染性或康复的人时会被感染，一旦被感染，它们就会在暴露的和有传染性的人群中传播。这两个物种都遵循逻辑种群模型，人类有迁移和疾病导致的死亡。我们用繁殖数R-0来表示一个受感染个体在感染期间引起的继发病例数。我们发现无病平衡点在R-0 < 1时是局部渐近稳定的，在R-0 < 1时是不稳定的。我们证明了所有R-0 bbb1至少存在一个地方性平衡点。在没有疾病引起的死亡的情况下，我们证明了在R-0 = 1处的跨临界分岔是超临界的（正向的）。数值模拟表明，对于较大的病死率值，在R-0 = 1处可能出现亚临界（向后）分岔。
We present an ordinary differential equation mathematical model for the spread of malaria in human and mosquito populations. Susceptible humans can be infected when they are bitten by an infectious mosquito. They then progress through the exposed, infectious, and recovered classes, before reentering the susceptible class. Susceptible mosquitoes can become infected when they bite infectious or recovered humans, and once infected they move through the exposed and infectious classes. Both species follow a logistic population model, with humans having immigration and disease- induced death. We de. ne a reproductive number, R-0, for the number of secondary cases that one infected individual will cause through the duration of the infectious period. We find that the disease- free equilibrium is locally asymptotically stable when R-0 < 1 and unstable when R-0 > 1. We prove the existence of at least one endemic equilibrium point for all R-0 > 1. In the absence of disease- induced death, we prove that the transcritical bifurcation at R-0 = 1 is supercritical (forward). Numerical simulations show that for larger values of the disease- induced death rate, a subcritical (backward) bifurcation is possible at R-0 = 1.