Omame A, Rwezaura H, Diagne M L, Inyama S C, Tchuenche J M
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Mathematics Department, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, Tanzania.
Eur Phys J Plus. 2021;136(10):1090. doi: 10.1140/epjp/s13360-021-02030-6. Epub 2021 Oct 29.
A mathematical model for the co-interaction of COVID-19 and dengue transmission dynamics is formulated and analyzed. The sub-models are shown to be locally asymptotically stable when the respective reproduction numbers are below unity. Using available data sets, the model is fitted to the cumulative confirmed daily COVID-19 cases and deaths for Brazil () from February 1, 2021 to September 20, 2021. The fitting was done using the function in the Optimization Toolbox of MATLAB. Parameters denoting the COVID-19 contact rate, death rate and loss of infection acquired immunity to COVID-19 were estimated using the two data sets. The model is then extended to include optimal control strategies. The appropriate conditions for the existence of optimal control and the optimality system for the co-infection model are established using the Pontryagin's Principle. Different control strategies and their cost-effectiveness analyses were considered and simulated for the model, which include: controls against incident dengue and COVID-19 infections, control against co-infection with a second disease and treatment controls for both dengue and COVID-19. Highlights of the simulation results show that: (1) dengue prevention strategy could avert as much as 870,000 new COVID-19 infections; (2) dengue only control strategy or COVID-19 only control strategy significantly reduces new co-infection cases; (3) the strategy implementing control against incident dengue infection is the most cost-effective in controlling dengue and COVID-19 co-infections.
建立并分析了一个关于新冠病毒（COVID - 19）与登革热传播动力学共同相互作用的数学模型。当各自的再生数低于1时，子模型被证明是局部渐近稳定的。利用可用数据集，该模型被拟合到2021年2月1日至2021年9月20日巴西的每日新冠累计确诊病例和死亡数据。拟合是使用MATLAB优化工具箱中的函数完成的。使用这两个数据集估计了表示新冠病毒接触率、死亡率以及对新冠病毒获得性免疫丧失的参数。然后该模型被扩展以纳入最优控制策略。利用庞特里亚金原理建立了最优控制存在的适当条件以及共感染模型的最优性系统。针对该模型考虑并模拟了不同的控制策略及其成本效益分析，其中包括：针对登革热和新冠病毒感染的控制、针对与第二种疾病共感染的控制以及针对登革热和新冠病毒的治疗控制。模拟结果的要点表明：（1）登革热预防策略可避免多达87万例新的新冠病毒感染；（2）仅登革热控制策略或仅新冠病毒控制策略可显著减少新的共感染病例；（3）实施针对登革热感染控制的策略在控制登革热和新冠病毒共感染方面最具成本效益。
