In this work, we develop and analyze a mathematical model for the dynamics of COVID-19 with re-infection in order to assess the impact of prior comorbidity (specifically, diabetes mellitus) on COVID-19 complications. The model is simulated using data relevant to the dynamics of the diseases in Lagos, Nigeria, making predictions for the attainment of peak periods in the presence or absence of comorbidity. The model is shown to undergo the phenomenon of backward bifurcation caused by the parameter accounting for increased susceptibility to COVID-19 infection by comorbid susceptibles as well as the rate of reinfection by those who have recovered from a previous COVID-19 infection. Simulations of the cumulative number of active cases (including those with comorbidity), at different reinfection rates, show infection peaks reducing with decreasing reinfection of those who have recovered from a previous COVID-19 infection. In addition, optimal control and cost-effectiveness analysis of the model reveal that the strategy that prevents COVID-19 infection by comorbid susceptibles is the most cost-effective of all the control strategies for the prevention of COVID-19.

中文翻译：

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具有优化控制的 COVID-19 和合并症共感染模型分析

在这项工作中，我们开发和分析了 COVID-19 再感染动态的数学模型，以评估先前合并症（特别是糖尿病）的影响) 关于 COVID-19 并发症。该模型使用与尼日利亚拉各斯疾病动态相关的数据进行模拟，预测在存在或不存在合并症的情况下达到高峰期。该模型显示出经历了由参数引起的后向分叉现象，该参数说明共病易感者对 COVID-19 感染的易感性增加，以及从先前 COVID-19 感染中恢复的人的再感染率。对不同再感染率的活动病例（包括合并症患者）的累积数量进行的模拟显示，随着从先前 COVID-19 感染中恢复的患者的再感染减少，感染峰值会降低。此外，