Malaria and COVID-19 co-dynamics: A mathematical model and optimal control.
Malaria and COVID-19 co-dynamics: A mathematical model and optimal control.
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DOI：
10.1016/j.apm.2021.06.016
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发表时间：
2021-11
影响因子：
5
通讯作者：
Tchuenche JM
中科院分区：
文献类型：
--
作者：
Tchoumi SY;Diagne ML;Rwezaura H;Tchuenche JM
疟疾是已知最久的病媒传播疾病之一，在世界热带和亚热带地区构成重大健康问题。目前，新出现的COVID-19大流行及其第二波和即将到来的第三波的威胁加剧了其复杂性。我们制定和分析了一个数学模型，该模型结合了疟疾和COVID-19共同动力学的一些流行病学特征。得到了仅疟疾子模型和仅COVID-19子模型平衡点稳定的充分条件。仅COVID-19子模型具有全局渐近稳定的平衡点，而在一定条件下，只要子模型再生数小于1，仅疟疾子模型就会发生后向分支现象。对偶疟疾-COVID 19模型的平衡点是局部渐近稳定的，因为由于可能发生向后分支而排除了全局稳定性。最优控制的完整的模型，以减轻这两种疾病的传播和他们的共同感染。应用庞特里亚金最大值原理建立了最优控制问题的存在性，并导出了病害最优控制的必要条件。虽然这不是一个案例研究，但支持最佳控制理论分析的模拟结果表明，随着世界继续应对这场前所未有的COVID-19大流行，与单独应用每种预防性控制措施相比，同时应用疟疾和COVID-19保护措施可能有助于减缓其传播。
Malaria, one of the longest-known vector-borne diseases, poses a major health problem in tropical and subtropical regions of the world. Its complexity is currently being exacerbated by the emerging COVID-19 pandemic and the threats of its second wave and looming third wave. We formulate and analyze a mathematical model incorporating some epidemiological features of the co-dynamics of both malaria and COVID-19. Sufficient conditions for the stability of the malaria only and COVID-19 only sub-models’ equilibria are derived. The COVID-19 only sub-model has globally asymptotically stable equilibria while under certain condition, the malaria-only could undergo the phenomenon of backward bifurcation whenever the sub-model reproduction number is less than unity. The equilibria of the dual malaria-COVID19 model are locally asymptotically stable as global stability is precluded owing to the possible occurrence of backward bifurcation. Optimal control of the full model to mitigate the spread of both diseases and their co-infection are derived. Pontryagin’s Maximum Principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions for optimal control of the diseases. Though this is not a case study, simulation results to support theoretical analysis of the optimal control suggests that concurrently applying malaria and COVID-19 protective measures could help mitigate their spread compared to applying each preventive control measure singly as the world continues to deal with this unprecedented and unparalleled COVID-19 pandemic.
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