Design and Investigation of Mathematical Model for the Vaccination and Transmission of Monkeypox Virus without Lifelong Immunity

S K Tiwari; P Porwal; Neha Mangal

doi:10.17485/IJST/v16i39.1521

Article

Design and Investigation of Mathematical Model for the Vaccination and Transmission of Monkeypox Virus without Lifelong Immunity

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i39.1521

Year: 2023, Volume: 16, Issue: 39, Pages: 3423-3434

Original Article

Design and Investigation of Mathematical Model for the Vaccination and Transmission of Monkeypox Virus without Lifelong Immunity

S K Tiwari¹, P Porwal², Neha Mangal^3*

¹Head, School of Studies in Mathematics, Vikram University, Ujjain, 456010, M.P., India
²Assistant Professor, School of Studies in Mathematics, Vikram University, Ujjain, 456010, M.P., India
³Research Scholar, School of Studies in Mathematics, Vikram University, Ujjain, 456010, M.P., India

*Corresponding Author
Email: [email protected]

Received Date:19 June 2023, Accepted Date:15 September 2023, Published Date:25 October 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: For the purpose of evaluating the potential for outbreaks of monkeypox (MPX) in a metropolitan region and defining necessary public health measures to restrict the spread of the virus through the use of a model of its dissemination, the preventive interventions have a critical role in the management of infectious diseases. The objective of this study is to assess the feasibility of managing and eliminating MPX through the use of voluntary vaccination and treatment measures. Methods: We developed two equilibriums for the model, endemic and disease-free, via standard methods. Using the comparison theorem and the next-generation matrix, it was demonstrated that the DFE is both locally and globally asymptotically stable if R0 < 1. By using linearization approach, the endemic equilibrium point only occurred when R0 > 1. Through the utilization of model and sensitivity analysis techniques, we are able to discern the pivotal public health elements and afterwards show several scenarios based on distinct transmission assumptions. Findings: Based on the findings of the study, implementing measures to isolate individuals with diseases from the wider community can effectively mitigate the transmission of diseases. A comprehensive examination of the model parameters using sensitivity analysis indicates that when the treatment and vaccination control parameters are augmented, there is a decrease in the fundamental reproduction numbers of the model. These reproduction numbers serve as a crucial threshold for identifying new infections within host populations. Novelty: Our research highlights the importance of treatment, vaccination, and public understanding as the exclusive preventive measures in the context of monkeypox. Furthermore, our analysis led us to the determination that disease can be managed and controlled, but achieving lasting immunity is not yet possible, given the absence of definitive treatments and vaccination for monkeypox infection. 2010 Mathematics Subject Classification: 81T99, 93A30.

Keywords: Monkeypox, Basic reproduction number, Comparison theorem, Sensitivity analysis, Stablity analysis

References

National Center for Emerging and Zoonotic Infectious Diseases(NCEZID), Division of High-Consequence Pathogens and Pathology (DHCPP), Monkeypox. Centers for Disease Control and Prevention. Available from: https://www.cdc.gov/poxvirus/monkeypox/index.html (accessed 2021-November-10)
Alakunle E, Moens U, Nchinda G, Okeke MI. Monkeypox Virus in Nigeria: Infection Biology, Epidemiology, and Evolution. Viruses. 2020;12(11):1–29. Available from: https://doi.org/10.3390/v12111257
Of IG. Guidelines for management of monkeypox disease. Government of India. Ministry of Health and Family Welfare. Available from: https://main.mohfw.gov.in/?q=diseasealerts-0 (accessed 2022-June-6)
What you should know about Monkeypox. Centers for Disease Control and Prevention (U.S.). Available from: https://stacks.cdc.gov/view/cdc/26229
National Center for Emerging and Zoonotic Infectious Diseases (NCEZID), Division of High-Consequence Pathogens and Pathology (DHCPP), Monkeypox. Centers for Disease Control and Prevention. 2022. Available from: https://www.cdc.gov/poxvirus/Mpox/reponse/2022/ index.html
Kozlov M. Monkeypox goes global: why scientists are on alert. Nature. 2022;606:15–16. Available from: https://doi.org/10.1038/d41586-022-01421-8
Multi-country monkeypox outbreak in non-endemic countries. WHO. Available from: https://www.who.int/emergencies/disease-outbreak-news/item/2022-DON385
Nguyen PY, Ajisegiri WS, Costantino V, Chughtai AA, Macintyre CR. Reemergence of Human Monkeypox and Declining Population Immunity in the Context of Urbanization, Nigeria, 2017–2020. Emerging Infectious Diseases. 2021;27(4):1007–1014. Available from: https://wwwnc.cdc.gov/eid/article/27/4/20-3569_article
Bunge EM, Hoet B, Chen L, Lienert F, Weidenthaler H, Baer LR, et al. The changing epidemiology of human monkeypox-A potential threat? A systematic review. PLoS Neglected Tropical Diseases. 2022;16(2):1–20. Available from: https://doi.org/10.1371/journal.pntd.0010141
Brand SPC, Cavallaro M, Cumming F, Turner C, Florence I, Blomquist P, et al. The role of vaccination and public awareness in forecasts of Mpox incidence in the United Kingdom. Nature Communications. 2023;14:1–12. Available from: https://doi.org/10.1038/s41467-023-38816-8
Meyer H, Ehmann R, Smith GL. Smallpox in the Post-Eradication Era. Viruses. 2020;12(2):1–11. Available from: https://doi.org/10.3390/v12020138
Beer EM, Rao VB. A systematic review of the epidemiology of human monkeypox outbreaks and implications for outbreak strategy. PLOS Neglected Tropical Diseases. 2019;13(10):1–20. Available from: https://doi.org/10.1371/journal.pntd.0007791
Olumuyiwa JP, Sumit K, Nitu K, Festus AO, Kayode O, Rabiu M. Transmission dynamics of Monkeypox virus: a mathematical modelling approach. Modeling Earth Systems and Environment. 2022;8:3423–3434. Available from: https://doi.org/10.1007/s40808-021-01313-2
Ngungu M, Addai E, Adeniji A, Adam UM, Oshinubi K. Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom. Frontiers in Public Health. 2023;11:1–16. Available from: https://doi.org/10.3389/fpubh.2023.1101436
Bankuru SV, Kossol S, Hou W, Mahmoudi P, Rychtář J, Taylor D. A game-theoretic model of Monkeypox to assess vaccination strategies. PeerJ. 2020;8:1–22. Available from: https://doi.org/10.7717/peerj.9272
Olumuyiwa JP, Oguntolu FA, Ojo MM, Oyeniyi AO, Jan R, Khan I. Fractional order mathematical model of monkeypox transmission dynamics. Phys. Scr. 2022;97:1–25. Available from: https://iopscience.iop.org/article/10.1088/1402-4896/ac7ebc/pdf
Alshehri A, Ullah S. Optimal control analysis of Monkeypox disease with the impact of environmental transmission. AIMS Mathematics. 2023;8(7):16926–16960. Available from: https://www.aimspress.com/article/doi/10.3934/math.2023865
TeWinkel RE. Stability analysis for the equilibria of a monkeypox model. University of Wisconsin thesis
Somma SA, Akinwande NI, Chado UD. A mathematical model of monkey pox virus transmission dynamics. Ife Journal of Science. 2019;21(1):195–204. Available from: https://doi.org/10.4314/ijs.v21i1.17
El-Mesady A, Elsonbaty A, Adel W. On nonlinear dynamics of a fractional order monkeypox virus model. Chaos, Solitons & Fractals. 2022;164:112716. Available from: https://doi.org/10.1016/j.chaos.2022.112716
Grant R, Nguyen LBLL, Breban R. Modelling human-to-human transmission of monkeypox. Bulletin of the World Health Organization. 2020;98(9):638–640. Available from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7463189/pdf/BLT.19.242347.pdf/
Risk assessment: Monkeypox multi-country outbreak. European Centre for Disease Prevention and Control. Available from: https://www.ecdc.europa.eu/en/publications-data/risk-assessment-monkeypox-multi-country-outbreak

Copyright

© 2023 Tiwari et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)