Tchuenche J M, Khamis S A, Agusto F B, Mpeshe S C
Mathematics Department, University of Dar es Salaam, Box 35062, Dar es Salaam, Tanzania.
Acta Biotheor. 2011 Mar;59(1):1-28. doi: 10.1007/s10441-010-9095-8. Epub 2010 Feb 7.
We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin's maximum principle, and it is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point.
我们使用两种预防方案（疫苗接种率的增加和降低）来构建和分析一个带有疫苗接种和治疗的流感大流行模型的动态情况。由于流感大流行具有季节性，我们在一个有限的时间间隔内研究其动态。我们主要专注于运用控制理论以可能的最小成本和副作用来控制疾病，因此通过庞特里亚金极大值原理来应用该理论，并且观察到在疫情爆发初期应在增加疫苗接种的同时全力进行治疗。接下来，进行敏感性分析和模拟（使用四阶龙格 - 库塔方法），以确定导致疾病传播和流行的不同因素的相对重要性。除死亡率外，各种繁殖数中最敏感的参数是流入率，而新兵比例和疫苗效力是地方病平衡点最敏感的参数。
