HIV and COVID-19 co-infection: A mathematical model and optimal control

N Ringa; M L Diagne; H Rwezaura; A Omame; S Y Tchoumi; J M Tchuenche

doi:10.1016/j.imu.2022.100978

HIV and COVID-19 co-infection: A mathematical model and optimal control

Inform Med Unlocked. 2022:31:100978. doi: 10.1016/j.imu.2022.100978. Epub 2022 May 30.

Authors

N Ringa^{1

2}, M L Diagne³, H Rwezaura⁴, A Omame^{5

6}, S Y Tchoumi⁷, J M Tchuenche^{8

9}

Affiliations

¹ Data and Analytic Services, British Columbia Centre for Disease Control, 655 W 12th Ave, Vancouver, BC, Canada V5Z 4R4.
² School of Population and Public Health, University of British Columbia, 2329 West Mall Vancouver, BC, Canada V6T 1Z4.
³ Département de Mathématiques, UFR des Sciences et Technologies, Université de Thiès, BP 967 Thiès, Senegal.
⁴ Mathematics Department, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, Tanzania.
⁵ Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
⁶ Abdus Salam School of Mathematical Sciences, Government College University Lahore, Pakistan.
⁷ Department of Mathematics and Computer Sciences ENSAI, University of Ngaoundéré, P.O. Box 455 Ngaoundéré, Cameroon.
⁸ School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa.
⁹ School of Computational and Communication Sciences and Engineering, Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania.

Abstract

A new mathematical model for COVID-19 and HIV/AIDS is considered to assess the impact of COVID-19 on HIV dynamics and vice-versa. Investigating the epidemiologic synergy between COVID-19 and HIV is important. The dynamics of the full model is driven by that of its sub-models; therefore, basic analysis of the two sub-models; HIV-only and COVID-19 only is carried out. The basic reproduction number is computed and used to prove local and global asymptotic stability of the sub-models' disease-free and endemic equilibria. Using the fmincon function in the Optimization Toolbox of MATLAB, the model is fitted to real COVID-19 data set from South Africa. The impact of intervention measures, namely, COVID-19 and HIV prevention interventions and COVID-19 treatment are incorporated into the model using time-dependent controls. It is observed that HIV prevention measures can significantly reduce the burden of co-infections with COVID-19, while effective treatment of COVID-19 could reduce co-infections with opportunistic infections such as HIV/AIDS. In particular, the COVID-19 only prevention strategy averted about 10,500 new co-infection cases, with similar number also averted by the HIV-only prevention control.

Keywords: Basic reproduction number; COVID-19; Co-infection; HIV; Optimal control.