Sardar Tridip, Rana Sourav, Bhattacharya Sabyasachi, Al-Khaled Kamel, Chattopadhyay Joydev
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata, 700108, West Bengal, India.
Department of Statistics, Visva-Bharati University, Santiniketan, West Bengal, India.
Math Biosci. 2015 May;263:18-36. doi: 10.1016/j.mbs.2015.01.009. Epub 2015 Jan 30.
In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R0, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R0, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector.
在本研究中，考虑了三种关于常见单菌株蚊媒传播疾病的数学模型。第一个基于常微分方程，另外两个模型基于分数阶微分方程。所提出的模型使用1999 - 2002年期间委内瑞拉两个省份已发表的每月登革热发病率数据进行验证。我们从数据中估计这些模型的几个参数，如分数阶导数的阶数（在两个分数阶系统的情况下）、蚊子的叮咬率、两个感染概率、蚊子繁殖率和死亡率等。使用数据估计了常微分方程系统的基本再生数(R_0)。对于两个分数阶系统，推导了(R_0)的上界，并使用已发表的数据获得其值。使用数据估计了这三个模型的感染力和有效再生数(R(t))。对蚊子记忆参数与一些重要响应进行了敏感性分析。我们使用赤池信息准则（AIC）来确定所提出的三个模型中最佳的模型。观察到宿主和媒介种群中都具有记忆的模型与流行数据具有更好的一致性。最后，我们利用宿主和媒介的记忆为蚊媒疾病登革热提供了一种控制策略。
