National Institute for Mathematical and Biological Synthesis (NIMBioS), University of Tennessee, Knoxville, TN 37996, USA.
Math Biosci. 2012 Nov;240(1):45-62. doi: 10.1016/j.mbs.2012.06.003. Epub 2012 Jun 23.
A deterministic ordinary differential equation model for the dynamics of malaria transmission that explicitly integrates the demography and life style of the malaria vector and its interaction with the human population is developed and analyzed. The model is different from standard malaria transmission models in that the vectors involved in disease transmission are those that are questing for human blood. Model results indicate the existence of nontrivial disease free and endemic steady states, which can be driven to instability via a Hopf bifurcation as a parameter is varied in parameter space. Our model therefore captures oscillations that are known to exist in the dynamics of malaria transmission without recourse to external seasonal forcing. Additionally, our model exhibits the phenomenon of backward bifurcation. Two threshold parameters that can be used for purposes of control are identified and studied, and possible reasons why it has been difficult to eradicate malaria are advanced.
建立并分析了一个疟疾传播动力学的确定性常微分方程模型，该模型明确地整合了疟疾媒介的人口统计学和生活方式及其与人类群体的相互作用。与标准疟疾传播模型不同，该模型涉及的媒介是那些正在寻找人类血液的媒介。模型结果表明，存在非平凡的无病和地方性稳定状态，随着参数在参数空间中的变化，可以通过Hopf 分支将其驱动到不稳定状态。因此，我们的模型可以捕捉到疟疾传播动力学中已知存在的振荡，而无需诉诸外部季节性驱动。此外，我们的模型还表现出向后分歧的现象。确定并研究了两个可用于控制目的的阈值参数，并提出了难以根除疟疾的可能原因。
