Abidemi Afeez, Aziz Nur Arina Bazilah
Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia; Department of Mathematical Sciences, Federal University of Technology, Akure, P.M.B. 704, Ondo State, Nigeria.
Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia.
Comput Methods Programs Biomed. 2020 Nov;196:105585. doi: 10.1016/j.cmpb.2020.105585. Epub 2020 Jun 5.
Background Dengue is a vector-borne viral disease endemic in Malaysia. The disease is presently a public health issue in the country. Hence, the use of mathematical model to gain insights into the transmission dynamics and derive the optimal control strategies for minimizing the spread of the disease is of great importance. Methods A model involving eight mutually exclusive compartments with the introduction of personal protection, larvicide and adulticide control strategies describing dengue fever transmission dynamics is presented. The control-induced basic reproduction number (R˜) related to the model is computed using the next generation matrix method. Comparison theorem is used to analyse the global dynamics of the model. The model is fitted to the data related to the 2012 dengue outbreak in Johor, Malaysia, using the least-squares method. In a bid to optimally curtail dengue fever propagation, we apply optimal control theory to investigate the effect of several control strategies of combination of optimal personal protection, larvicide and adulticide controls on dengue fever dynamics. The resulting optimality system is simulated in MATLAB using fourth order Runge-Kutta scheme based on the forward-backward sweep method. In addition, cost-effectiveness analysis is performed to determine the most cost-effective strategy among the various control strategies analysed. Results Analysis of the model with control parameters shows that the model has two disease-free equilibria, namely, trivial equilibrium and biologically realistic disease-free equilibrium, and one endemic equilibrium point. It also reveals that the biologically realistic disease-free equilibrium is both locally and globally asymptotically stable whenever the inequality R˜<1holds. In the case of model with time-dependent control functions, the optimality levels of the three control functions required to optimally control dengue disease transmission are derived. Conclusion We conclude that dengue fever transmission can be curtailed by adopting any of the several control strategies analysed in this study. Furthermore, a strategy which combines personal protection and adulticide controls is found to be the most cost-effective control strategy.
登革热是一种由媒介传播的病毒性疾病，在马来西亚流行。目前，该疾病是该国的一个公共卫生问题。因此，使用数学模型来深入了解传播动态并推导使疾病传播最小化的最优控制策略非常重要。方法：提出了一个包含八个相互排斥隔室的模型，引入了个人防护、杀幼虫剂和杀成虫剂控制策略来描述登革热传播动态。使用下一代矩阵方法计算与该模型相关的控制诱导基本再生数（(R˜)）。比较定理用于分析模型的全局动态。使用最小二乘法将该模型拟合到与2012年马来西亚柔佛州登革热疫情相关的数据。为了最优地减少登革热传播，我们应用最优控制理论来研究最优个人防护、杀幼虫剂和杀成虫剂控制组合的几种控制策略对登革热动态的影响。基于前向 - 后向扫描方法，使用四阶龙格 - 库塔方案在MATLAB中模拟所得的最优性系统。此外，进行成本效益分析以确定所分析的各种控制策略中最具成本效益的策略。结果：对具有控制参数的模型分析表明，该模型有两个无病平衡点，即平凡平衡点和生物学上现实的无病平衡点，以及一个地方病平衡点。还表明，只要不等式(R˜<1)成立，生物学上现实的无病平衡点在局部和全局都是渐近稳定的。对于具有时间依赖控制函数的模型，推导了最优控制登革热疾病传播所需的三种控制函数的最优水平。结论：我们得出结论，通过采用本研究中分析的几种控制策略中的任何一种，都可以减少登革热传播。此外，发现将个人防护和杀成虫剂控制相结合的策略是最具成本效益的控制策略。
