Analysis of COVID-19 and comorbidity co-infection model with optimal control

Andrew Omame; Ndolane Sene; Ikenna Nometa; Cosmas I Nwakanma; Emmanuel U Nwafor; Nneka O Iheonu; Daniel Okuonghae

doi:10.1002/oca.2748

Analysis of COVID-19 and comorbidity co-infection model with optimal control

Optim Control Appl Methods. 2021 Nov-Dec;42(6):1568-1590. doi: 10.1002/oca.2748. Epub 2021 Jun 2.

Authors

Andrew Omame¹, Ndolane Sene², Ikenna Nometa³, Cosmas I Nwakanma⁴, Emmanuel U Nwafor¹, Nneka O Iheonu¹, Daniel Okuonghae⁵

Affiliations

¹ Department of Mathematics Federal University of Technology Owerri Owerri Nigeria.
² Laboratoire Lmdan, Département de Mathématiques de la Décision, Facultédes Sciences Economiques et Gestion Université Cheikh Anta Diop de Dakar Dakar Fann Senegal.
³ Department of Mathematics University of Hawaii Manoa Honolulu Hawaii USA.
⁴ Networked Systems Lab, IT Covergence Engineering, School of Electronic Engineering Kumoh National Institute of Technology Gumi Korea.
⁵ Department of Mathematics University of Benin Benin City Nigeria.

Abstract

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.

Keywords: COVID‐19; comorbidity; data‐fitting; optimal control; reinfection.