Analysis of COVID-19 and comorbidity co-infection Model with Optimal Control

Abstract

The new coronavirus disease 2019 (COVID-19) infection is a double challenge for people infected with comorbidities such as cardiovascular and cerebrovascular diseases and diabetes. Comorbidities have been reported to be risk factors for the complications of COVID-19. In this work, we develop and analyze a mathematical model for the dynamics of COVID-19 infection in order to assess the impacts of prior comorbidity on COVID-19 complications and COVID-19 re-infection. 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 re-infection by those who have recovered from a previous COVID-19 infection. Sensitivity analysis of the model when the population of individuals co-infected with COVID-19 and comorbidity is used as response function revealed that the top ranked parameters that drive the dynamics of the co-infection model are the effective contact rate for COVID-19 transmission, $\beta\sst{cv}$, the parameter accounting for increased susceptibility to COVID-19 by comorbid susceptibles, $\chi\sst{cm}$, the comorbidity development rate, $\theta\sst{cm}$, the detection rate for singly infected and co-infected individuals, $\eta_1$ and $\eta_2$, as well as the recovery rate from COVID-19 for co-infected individuals, $\varphi\sst{i2}$. Simulations of the model reveal that the cumulative confirmed cases (without comorbidity) may get up to 180,000 after 200 days, if the hyper susceptibility rate of comorbid susceptibles is as high as 1.2 per day. Also, the cumulative confirmed cases (including those co-infected with comorbidity) may be as high as 1000,000 cases by the end of November, 2020 if the re-infection rates for COVID-19 is 0.1 per day. It may be worse than this if the re-infection rates increase higher. Moreover, if policies are strictly put in place to step down the probability of COVID-19 infection by comorbid susceptibles to as low as 0.4 per day and step up the detection rate for singly infected individuals to 0.7 per day, then the reproduction number can be brought very low below one, and COVID-19 infection eliminated from the population. In addition, optimal control and cost-effectiveness analysis of the model reveal that the the strategy that prevents COVID-19 infection by comorbid susceptibles has the least ICER and is the most cost-effective of all the control strategies for the prevention of COVID-19.

Optimal Control and Cost-Effectiveness Analysis of an HPV–Chlamydia trachomatis Co-infection Model

“…Mathematical modelling has been used extensively in studying the behaviour of infectious diseases, including their co-infections [1,7,13,18,23,28,41,43,44]. Particularly, Several mathematical models have been developed to understand the transmission dyanamics of Chlamydia trachomatis infections.…”

A co‐infection model for oncogenic human papillomavirus and tuberculosis with optimal control and Cost‐Effectiveness Analysis

“…Lately, mathematical models have been developed, incorporating optimal control strategies for the dynamics of infectious diseases, including their co-infections. [25][26][27][28][29][30][31][32][33][34] More recently, Egeonu et al 27 studied a co-infection model for drug-resistant malaria and cholera with optimal control. Numerical simulations of their model revealed that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.…”

A co-infection model for Oncogenic HPV and TB with Optimal Control and Cost-Effectiveness Analysis

“…Lately, mathematical models have been developed to consider the optimal control strategies for the dynamics of infectious diseases including their co-infections [1, 9, 11, 20, 26, 27, 31, 32, 34]. Agusto and Adekunle [1] studied the optimal control and cost-effectiveness analysis of the co-infection of drug-resistant tuberculosis and HIV/AIDS.…”