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A mathematical model for the co-dynamics of COVID-19 and tuberculosis

Author

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  • Ojo, Mayowa M.
  • Peter, Olumuyiwa James
  • Goufo, Emile Franc Doungmo
  • Nisar, Kottakkaran Sooppy

Abstract

In this study, we formulated and analyzed a deterministic mathematical model for the co-infection of COVID-19 and tuberculosis, to study the co-dynamics and impact of each disease in a given population. Using each disease’s corresponding reproduction number, the existence and stability of the disease-free equilibrium were established. When the respective threshold quantities RC, and RT are below unity, the COVID-19 and TB-free equilibrium are said to be locally asymptotically stable. The impact of vaccine (i.e., efficacy and vaccinated proportion) and the condition required for COVID-19 eradication was examined. Furthermore, the presence of the endemic equilibria of the sub-models is analyzed and the criteria for the phenomenon of backward bifurcation of the COVID-19 sub-model are presented. To better understand how each disease condition impacts the dynamics behavior of the other, we investigate the invasion criterion of each disease by computing the threshold quantity known as the invasion reproduction number. We perform a numerical simulation to investigate the impact of threshold quantities (RC,RT) with respect to their invasion reproduction number, co-infection transmission rate (βct), and each disease transmission rate (βc,βt) on disease dynamics. The outcomes established the necessity for the coexistence or elimination of both diseases from the communities. Overall, our findings imply that while COVID-19 incidence decreases with co-infection prevalence, the burden of tuberculosis on the human population increases.

Suggested Citation

  • Ojo, Mayowa M. & Peter, Olumuyiwa James & Goufo, Emile Franc Doungmo & Nisar, Kottakkaran Sooppy, 2023. "A mathematical model for the co-dynamics of COVID-19 and tuberculosis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 499-520.
    • Handle: RePEc:eee:matcom:v:207:y:2023:i:c:p:499-520
    DOI: 10.1016/j.matcom.2023.01.014
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    References listed on IDEAS

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    1. Ojo, Mayowa M. & Benson, Temitope O. & Peter, Olumuyiwa James & Goufo, Emile Franc Doungmo, 2022. "Nonlinear optimal control strategies for a mathematical model of COVID-19 and influenza co-infection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    2. Felipe Lima dos Santos & Ludmilla Leidianne Limirio Souza & Alexandre Tadashi Inomata Bruce & Juliane de Almeida Crispim & Luiz Henrique Arroyo & Antônio Carlos Vieira Ramos & Thaís Zamboni Berra & Ya, 2021. "Patients’ perceptions regarding multidrug-resistant tuberculosis and barriers to seeking care in a priority city in Brazil during COVID-19 pandemic: A qualitative study," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-19, April.
    3. Bandekar, Shraddha Ramdas & Ghosh, Mini, 2022. "A co-infection model on TB - COVID-19 with optimal control and sensitivity analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 1-31.
    4. Omame, A. & Abbas, M. & Onyenegecha, C.P., 2021. "A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    5. Kassahun Getnet Mekonen & Shiferaw Feyissa Balcha & Legesse Lemecha Obsu & Abdulkadir Hassen, 2022. "Mathematical Modeling and Analysis of TB and COVID-19 Coinfection," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-20, March.
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