A MATHEMATICAL MODEL FOR THE DYNAMICS OF COVID-19 AND MONKEYPOX CO-INFECTION CONSIDERING THE EFFECTS OF VACCINATION, QUARANTINE, AND REINFECTION
Keywords:
COVID-19; Monkeypox; Co-infection dynamics; Vaccination; Lyapunov functions; Mortality reduction.Abstract
A deterministic compartment model for the co-infection of COVID-19 and Monkeypox taking into account vaccination, quarantine, treatment, and reinfection is introduced. It is demonstrated that the compartment model is mathematically well-posed. The disease-free equilibrium and local stability are obtained. The basic reproduction number $R_0$ is determined. The global stability result for the disease-free equilibrium is proven using the Castillo-Chavez and Song method. A Lyapunov function is introduced based on which it establishes global stability for endemic equilibrium. A critical modifying variable, $\eta [0,1].$ denoting the efficacy of treatment per session against mortality, is explored. Simulation outcomes indicate that low $\eta$ (i.e when $\eta = 0$, there is Effective treatment) decreases mortality but enhances long-term treatment efforts, and high $\eta$ (i.e when $\eta = 1$, there is Ineffective treatment) deteriorates survival rates among the treated category. Results obtained from subsequent simulations indicate that COVID-19 exerts a postponing effect on Monkeypox infections due to its influence on enhancing the reproduction number and boosting co-infections.
These findings bring out the need to incorporate vaccine, quarantine, and treatment against dual outbreaks of Covid-19 and Monkeypox.
Downloads
References
%chapter{REFERENCES}
%bibliographystyle{}
begin{thebibliography}{100}
bibitem{Hoffmann2020}
Markus Hoffmann, Hannah Kleine-Weber, Simon Schroeder, Nadine Krüger, Tanja Herrler, Sandra Erichsen, Tobias S. Schiergens, and others (2020).
textit{SARS-CoV-2 cell entry depends on ACE2 and TMPRSS2 and is blocked by a clinically proven protease inhibitor}.
Cell, 181(2), 271--280.
bibitem{Andersen2020}
Kristian G. Andersen, Andrew Rambaut, W. Ian Lipkin, Edward C. Holmes, and Robert F. Garry (2020).
textit{The proximal origin of SARS-CoV-2}.
Nature Medicine, 26, 450--452.
bibitem{Hill2013}
Andrew Hill (2013).
textit{The ecology and evolution of zoonotic diseases}.
Proceedings of the National Academy of Sciences (PNAS), 110(20), 8399--8400.
bibitem{Liu2020}
Ying Liu, Albert A. Gayle, Annelies Wilder-Smith, and Joacim Rocklöv (2020).
textit{The reproductive number of COVID-19 is higher compared to SARS coronavirus}.
Journal of Travel Medicine, 27(2).
bibitem{Guan2020}
Wei-jie Guan, Zheng-yi Ni, Yu Hu, Wen-hua Liang, Chun-quan Ou, Jian-xing He, Lei Liu, Hong Shan, Chun-liang Lei,and others (2020).
textit{Clinical characteristics of coronavirus disease 2019 in China}.
New England Journal of Medicine, 382, 1708--1720.
bibitem{Wiersinga2020}
W. Joost Wiersinga, Andrew Rhodes, Allen C. Cheng, Sharon J. Peacock, and Hallie C. Prescott (2020).
textit{Pathophysiology, transmission, diagnosis, and treatment of COVID-19: A review}.
JAMA, 324(8), 782--793.
bibitem{Ladnyj1972}
I. D. Ladnyj, P. Ziegler, and E. Kima (1972).
textit{A human infection caused by monkeypox virus in Basankusu Territory, Democratic Republic of the Congo}.
Bulletin of the World Health Organization, 46, 593--597.
bibitem{Likos2005}
Anne M. Likos, Suzanne A. Sammons, Victoria A. Olson, Andrea M. Frace, Yvonne Li, Margarita Olsen-Rasmussen, William Davidson, John A. G. Smith, Richard L. Regnery, and Inger K. Damon (2005).
textit{A tale of two clades: Monkeypox viruses}.
Journal of General Virology, 86, 2661--2672.
bibitem{CDC2022}
Centers for Disease Control and Prevention (2022).
textit{Monkeypox: Epidemiology, transmission, and outbreaks}.
CDC.gov.
bibitem{Reynolds2006}
Mary G. Reynolds, Kazunori Yorita, Michael J. Kuehnert, William B. Davidson, Victoria A. Huhn, John A. Holman, and Inger K. Damon (2006).
textit{Clinical manifestations of human monkeypox influenced by route of infection}.
Journal of Infectious Diseases, 194(6), 773--780.
bibitem{Reed2004}
Kurt D. Reed, Joseph W. Melski, Mark B. Graham, John M. Regnery, Michael J. Sotir, Maureen Wegner, David L. Kazmierczak, and others (2004).
textit{The detection of monkeypox in the United States}.
New England Journal of Medicine, 350, 342--350.
bibitem{Kraemer2022}
Moritz U. G. Kraemer, Houriiyah Tegally, David M. Pigott, Bernard M. Greenwood, Oliver G. Pybus, and Samuel V. Scarpino (2022).
textit{The 2022 global mpox outbreak: Epidemiology and implications}.
The Lancet Infectious Diseases, 22, 1112--1121.
bibitem{WHO2022a}
World Health Organization (2022a).
textit{Multi-country monkeypox outbreak: Situation update}.
WHO.int.
bibitem{BenitesZapata2023}
Víctor A. Benites-Zapata, Jhony A. Ulloque-Badaracco, Percy L. Alarcon-Braga, Diego Hernandez-Bustamante, and Carlos A. Rodriguez-Morales (2023).
textit{Clinical challenges in co-infection with COVID-19 and Monkeypox}.
Travel Medicine and Infectious Disease, 52.
bibitem{Vabret2020}
Nicolas Vabret, Gregory J. Britton, Conor Gruber, Samarth Hegde, Jonghyeon Kim, Maria Kuksin, Roman Levantovsky, Laura Malle, Javier Moreira, Marisa D. Park, Anna Pia, Esther Racanelli, Thomas J. Smith, Olivia S. Zaid, and Miriam Merad (2020).
textit{Immunology of COVID-19}.
Immunity, 52(6), 910--941.
bibitem{Patel2022}
Anupam Patel, Julia Bilinska, Joanna C. Tam, Matthew Da Silva Filho, and Christina Pagel (2022).
textit{Vaccination and prevention strategies for Monkeypox and COVID-19 co-circulation}.
BMJ Global Health, 7(11).
bibitem{YinkaOgunleye2019}
Akin Oyewale Yinka-Ogunleye, Obafemi Aruna, Mohammed Dalhat, Babatunde Ogoina, Ifedayo McCollum, Peter Disu, Godwin Mamadu, Maryam Ahmed, Adesola Adeoye, Chukwuma Chukwuogo, Adesina M. Saleh, Patrick Nguku, Emmanuel Idris, and Oyewale Tomori (2019).
textit{Outbreak of human monkeypox in Nigeria in 2017--18: A clinical and epidemiological report}.
The Lancet Infectious Diseases, 19(8), 872--879.
bibitem{Acheneje2024}
Acheneje, F., Eze, F. C., & Onyeka, B. (2024).
textit{A mathematical model for COVID-19 and Monkeypox co-infection dynamics}.
(Preprint or Journal Reference).
bibitem{USCensus2020}
United States Census Bureau (2020).
newblock National population estimates.
newblock emph{U.S. Census Bureau}.
bibitem{DavisCalvet2002}
D.~E. Davis and E.~Calvet (2002).
newblock Rodent population dynamics and zoonotic disease transmission.
newblock emph{Journal of Mammalogy}, 83(2):357--369.
bibitem{Zhang2020}
Jing Zhang, Meimei Litvinova, Yilin Liang, Yaqing Wang, Shi Zhao, Qianqian Wu, Jing Wang, Shengjie Zhang, Zheng Chen, Yicong Li, Wei Wang, and Hongjie Yu (2020).
newblock Changes in contact patterns shape the dynamics of the COVID-19 outbreak in China.
newblock emph{Science}, 368(6498):1481--1486.
bibitem{UKHSA2022a}
UK Health Security Agency (2022).
newblock Epidemiology of monkeypox in England.
newblock emph{UKHSA Technical Report}.
bibitem{CDCAnimals2022}
Centers for Disease Control and Prevention (2022).
newblock Monkeypox in animals.
newblock emph{CDC}.
bibitem{AdaljaInglesby2022}
Amesh~A. Adalja and Thomas~V. Inglesby (2022).
newblock A novel international monkeypox outbreak.
newblock emph{Annals of Internal Medicine}, 175(8):1175--1176.
bibitem{Lauer2020}
Stephen~A. Lauer, Kyra~H. Grantz, Qifang Bi, Forrest~K. Jones, Qulu Zheng, Hannah~R. Meredith, Andrew~S. Azman, Nicholas~G. Reich, and Justin Lessler (2020).
newblock The incubation period of coronavirus disease 2019 (COVID-19).
newblock emph{Annals of Internal Medicine}, 172(9):577--582.
bibitem{Mathieu2024}
Edouard Mathieu, Hannah Ritchie, Charlie Rod'es-Guirao, Appel Mahdi, Lucas Gavrilov, Joe Hasell, Bobbie Macdonald, Saloni Dattani, Diana Beltekian, and Max Roser (2024).
newblock A global database of COVID-19 vaccinations.
newblock emph{Nature Human Behaviour}.
bibitem{CDCVaccine2022}
Centers for Disease Control and Prevention (2022).
newblock Monkeypox vaccine administration.
newblock emph{CDC}.
bibitem{Thompson2021}
Mark~G. Thompson, Jennifer~L. Burgess, Allison~L. Naleway, H. Keipp Talbot, Sarah~E. Yoon, Mark~E. Meece, Lisa~A. Olsho, Sharon~E. Irving, and Edward~A. Belongia (2021).
newblock Interim estimates of vaccine effectiveness of COVID-19 vaccines.
newblock emph{Morbidity and Mortality Weekly Report}, 70(13):495--500.
bibitem{UKHSA2022b}
UK Health Security Agency (2022).
newblock Monkeypox outbreak in England.
newblock emph{UKHSA Situation Report}.
bibitem{CDCCovidControl2020}
Centers for Disease Control and Prevention (2020).
newblock COVID-19 control and prevention.
newblock emph{CDC}.
bibitem{WHOMonkeypoxControl2022}
World Health Organization (2022).
newblock Monkeypox control guidelines.
newblock emph{WHO}.
bibitem{Patel2022}
Anupam Patel, Julia Bilinska, Anna Tam, Matthew Da~Silva~Filho, and Christina Pagel (2022).
newblock Clinical characteristics and outcomes of monkeypox and COVID-19 co-infections.
newblock emph{The Lancet Infectious Diseases}, 22(10):1483--1492.
bibitem{Stokes2020}
Erin~K. Stokes, Laura Zambrano, Kayla~N. Anderson, Elizabeth~P. Marder, Rachel Raz, Paul~J. Felix, Elizabeth~L. Tie, Katherine~E. Fullerton, and Michelle~A. Watson (2020).
newblock Coronavirus disease 2019 case surveillance.
newblock emph{MMWR}, 69(24):759--765.
bibitem{WHOCovidDashboard2022}
World Health Organization (2022).
newblock WHO COVID-19 dashboard.
newblock emph{WHO}.
bibitem{WHOMonkeypoxOutbreak2022}
World Health Organization (2022).
newblock Multi-country outbreak of monkeypox.
newblock emph{WHO}.
bibitem{AriasXu2021}
Elizabeth Arias and Jiaquan Xu (2021).
newblock United States life tables.
newblock emph{National Vital Statistics Reports}, 70(19):1--64.
bibitem{Goldberg2021}
Yair Goldberg, Micha Mandel, Paul Bar-On, Omri Bodenheimer, Laurence Freedman, Nir Haas, and Amir Huppert (2021).
newblock Waning immunity after the BNT162b2 vaccine.
newblock emph{New England Journal of Medicine}, 385(24):e85.
end{thebibliography}
Published
How to Cite
Issue
Section
Copyright (c) 2026 Frankline Eze
This work is licensed under a Creative Commons Attribution 4.0 International License.
