Analyzing Global Stability of M-Pox Disease Dynamics: Mathematical Insights into Detection and Treatment Strategies

DOI: https://doi.org/10.33003/jobasr-2023-v1i1-19

Olopade I. A.

Akinwumi T. O.

Philemon M. E.

Mohammed I. T.

Sangoniyi S. O.

Adeniran G. A.

Ajao S. O.

Bello B. O.

Adesanya A. O.

Abstract
In this research, a mathematical model is constructed to scrutinize the transmission patterns of monkeypox (mpox), with a specific emphasis on integrating the early detection of infected undetected individuals to curb its transmission. This research takes into account a range of factors influencing the propagation of monkeypox, encompassing population demographics, contact dynamics, and the efficacy of early detection of unidentified infected individuals. Employing the next-generation matrix method, the basic reproduction number(đť‘…0) is computed, revealing that the disease-free equilibrium state is locally asymptotically stable when(đť‘…0 < 1). This suggests that containment of monkeypox is achievable within a human populace where (đť‘…0) remains below one (1), yet it transitions to an endemic state when (đť‘…0) exceeds this critical value one (1). Furthermore, a sensitivity analysis is conducted to evaluate the robustness of our findings to variations in model parameters. Utilizing numerical simulations conducted via MAPLE 18, we demonstrate the significance of prompt identification and immediate intervention for infected individuals who may otherwise go undetected, in effectively diminishing the dynamic propagation of monkeypox. The results underscore the pivotal role of early detection in mitigating monkeypox outbreaks and curtailing transmission rates.
References
Alarcón J., Kim M., Terashita D., Davar K., Garrigues J. M., &Guccione J. P.(2023). An Mpox-Related Death in the United States. N Engl J Med, 388(13): 1246–1257. Adesanya A. O., Olopade I. A., Akanni J. O., Oladapo A. O. &Omoloye M. A.(2016b).Mathematical and Sensitivity Analysis of Efficacy of Condom on the Dynamical Transmission of Gonorrhoea Disease. Imperial Journal of Interdisciplinary Research (IJIR). 2(11): 368-375. Adesanya A.O., Olopade I. A., Akinwumi T. O. & Adesanya A. A. (2016). Mathematical Analysis of Early Treatment of Gonorrhea Infection. American International Journal of Research in Science, Technology, Engineering & Mathematics, 15(2). Adesola O. I., Oloruntoyin S. S., Emmanuel P. M., Temilade M. I., Adeyemi A. G., Oladele A. S., Mamman A. U., & Kareem A. A. (2024). Mathematical Modelling and Analyzing the Dynamics of Condom Efficacy and Compliance in the Spread of HIV/AIDS. Asian Research Journal of Current Science. 6(1): 54–65. Adesola O. I., Temilade M. I., Emmanuel P. M., Oladele A. S., Adeyemi A. G., Sunday S. & Olumuyiwa A. S. (2024). Mathematical Analysis of Optimal Control of Human Immunodeficiency Virus (HIV) Co-infection with Tuberculosis (TB). Asian Research Journal of Current Science, 6(1): 23–53. Adewale, S. O, Olopade, I. A., Adeniran, G. A., Mohammed, I. T. and Ajao, S. O. (2015a). Mathematical Analysis of Effects of Isolation On Ebola Transmission Dynamics. Researchjournali’s Journal of Mathematics. Vol. 2, No. 2. Pp. 1-20. Adewale S. O., Olopade I. A., Adeniran G. A., Mohammed I. T., & Ajao S. O. (2015b). Mathematical Analysis of Effects of Isolation on Ebola Transmission Dynamics. Researchjournali’s Journal of Mathematics. 2(2):1-20. Adewale S. O., Olopade I. A., & Adeniran G. A.(2015c). Mathematical Analysis of Diarrhea in the Presence of Vaccine. .International Journal of Scientific and Engineering Research. 6(12):396-404. Adewale S. O., Olopade I. A., Ajao S. O., & Mohammed I. T. (2016a). Mathematical Analysis of Sensitive Parameters on the Dynamical Spread of HIV.International Journal of Innovative Research in Science, Engineering and Technology. 5(5): 2624-2635. Adewale S. O., Olopade I. A.,Ajao S. O. & Adeniran, G. A. (2016b). Optimal Control Analysis of The Dynamical Spread Of Measles.International Journal of Research GRANTHAALAYAH. 4(5): 169-188. Adler H., Gould S., Hine P., Snell L. B., Wong W., &Houlihan C. F. (2022). Clinical features and management of human monkeypox: a retrospective observational study in the UK. Lancet Infectious Diseases. DOI: http://dx.doi.org/10.1016/S1473- 3099(22)00228-6 AjaoS. O., OlopadeI. A.,Akinwumi T. O., Adewale S. O., & Adesanya A. O. (2023).Understanding the Transmission Dynamics and Control of HIV Infection: A Mathematical Model Approach. Journal of the Nigerian Society of Physical Sciences. 5(2). Akinola E.I. Awoyemi B. E., Olopade I. A.,Falowo O. D., &Akinwumi T.O. (2021)Mathematical Analyssis of Diarrhea Model in the Presence of Vaccination and Treatment Waves with Sensitivity Analysis. Journal of Applied Science and Environmental Management. 25(7): 1077-1084. Akinwumi T. O., OlopadeI. A.,Adesanya A. O., & Alabi M. O. (2021). Mathematical Model for the Transmission of HIV/AIDS with Early Treatment. Journal of Advances in Mathematics and Computer Science. 36(5): 35-51. Bankuru S. V., Kossol S., Hou W., Mahmoudi P., Rychtář J., &Taylor D. (2020). A game-theoretic model of monkeypox to assess vaccination strategies. PeerJ. 8:e9272. Bhunu C., Garira W., &Magombedze G. (2009) Mathematical analysis of a two strain hiv/aids model with antiretroviral treatment. Acta Biotheor. 57(3):361–381. Bhunu C., &Mushayabasa S. (2011). Modelling the transmission dynamics of pox-like infections. IAENG Int J. 41(2):1–9 Brown K., &Leggat P. A. (2016). Human Monkeypox: Current State of Knowledge and Implications for the Future. Trop Med Infect Dis. 1(1).DOI:doi.org/10.3390/ tropicalmed1010008. Bunge E. M., Hoet B., Chen L., Lienert F., Weidenthaler H., &Baer L. R. (2022). The changing epidemiology of human monkeypox: A potential threat? A systematic review. PLoSNegl Trop Dis. 16(2):e0010141. DOI:https://journals.plos.org/plosntds/ article?id=10.1371/journal.pntd.0010141 Castillo-Chavez C.,& Song B. (2004). Dynamical models of tuberculosis and their applications. Math Biosci Eng 1(2). Centers for Disease Control and Prevention (CDC). Multistate outbreak of monkeypox--Illinois, Indiana, and Wisconsin. (2003). MMWR Morb Mortal Wkly Rep 13; 52(23) :37–40. Available from: https://www.ncbi.nlm.nih.gov/pubmed/12803191. Doty J. B., Malekani J., Kalemba L., Stanley W. T., Monroe B. P., Nakazawa Y. U., & Karem K. L., (2017). Assessing Monkeypox virus prevalence in small mammals at the human–animal interface in the Democratic Republic of the Congo. Viruses. 9(10) 283. DOI: 10.3390/v9100283. Hoff N. A., Doshi R. H., Colwell B., Kebela-Illunga B., Mukadi P., &Mossoko M. (2017). Evolution of a Disease Surveillance System: An Increase in Reporting of Human Monkeypox Disease in the Democratic Republic of the Congo, 2001-2013. Int J Trop Dis Health25(2). DOI: http://dx.doi.org/10.9734/IJTDH/2017/35885 Jezek Z., Grab B., Szczeniowski M. V., Paluku K. M., &Mutombo M. (1988). Human monkeypox: secondary attack rates. Bull World Health Organ. 66(4): 65–70. Larkin M. (2003). Monkeypox spreads as US publichealth system plays catch-up. Lancet Infect Dis. 3(8):461. DOI:http://dx.doi.org/10.1016/s1473-3099(03)00713-8 Markewitz N. F., DeLuca J., Kalejaiye A., Shidid S., Jain T., &Parikh P. (2023). Mpox-Associated Pneumonia: A Case Report. AIM Clinical Cases. 2(3):e220945. DOI: https://doi. org/10.7326/aimcc.2022.0945 Mitjà O., Alemany A., Marks M., Lezama J. I., Rodríguez-Aldama J. C.,& Torres M. S. (2023) Mpox in people with advanced HIV infection: a global case series. DOI: http://dx.doi.org/10.1016/S0140-6736(23)00273-8 Nguyen MT, Mentredy A, Schallhorn J, Chan M, Aung S, Doernberg S. B (2023). Isolated Ocular Mpox without Skin Lesions, United States. Emerg Infect Dis. 29(6). DOI: http:// dx.doi.org/10.3201/eid2906.230032 Nguyen P., Ajisegiri W., Costantino V., Chughtai A., &Maclntyre C. (2021). Reemergence of human monkeypox and declining population immunity in the context of urbanization, Nigeria, 2017–2020. Emerg Infect Dis. 27(4):1007–1014. Olopade I. A., Adesanya A. O.& Mohammed I. T. (2017). Mathematical Analysis of the Global Dynamics of an SVEIR Epidemic Model with Herd Immunity. International Journal of Science and Engineering Investigations. (IJSEI).6(69):141-148. Olopade I. A., Adesanya A. O.&Akinwumi T. O. (2021a). Mathematical Transmission of SEIR Epidemic Model with Natural Immunity.Asian Journal of Pure and Applied Mathematics. 3(1):19-29. Olopade I. A., Adewale S. O., MohammedI. T., Adeniran G. A., Ajao S. O.& Ogunsola A. W. (2021b). Effect of Effective Contact Tracing in Curtaining the Spread of Covid-19. Asian Journal of Research in Biosciences. 3(2):118-134. Olopade I. A., Adewale S. O., MohammedI. T., Ajao S. O., &Oyedemi O. T. (2016). Mathematical Analysis of the Role of Detection in the Dynamical Spread of HIVTB Co-infection. Journal of Advances in Mathematics. 11(10): 5715-5740. Olopade I. A., Ajao S. O., Adeniran G. A., Adamu A. K., Adewale S. O., &Aderele O. R. 2022. Mathematical Transmission of Tuberculosis (TB) with Detection of Infected Undetectected. Asian Journal of Research in Medicine and Medical Sciences. 4(1): 100- 119. Olopade I. A., Akinola E. I., Philemon M. E., Mohammed I. T., Ajao S. O., Sangoniyi S. O.,Adeniran G. A. (2024). Modeling the Mathematical Transmission of a Pneumonia Epidemic Model with Awareness. J. Appl. Sci. Environ. Manage. 28(2): 403-413. Peter O., Viriyapong R., Oguntolu F., Yosyingyong P., Edogbanya H., &MO A. (2020). Stability and optimal control analysis of anscir epidemic model. J Math Comput Sci 2020(1):2722–2753. Philemon M. E., Olopade I. A., &Ogbaji E. O. (2023). Mathematical Analysis of the Effect of Quarantine on the Dynamical Transmission of Monkey-Pox. Asian Journal of Pure and Applied Mathematics. 5(1): 473–492. Priyamvada L., Carson W. C., Ortega E., Navarra T., Tran S., &Smith T. G. (2022). Serological responses to the MVA-based JYNNEOS monkeypox vaccine in a cohort of participants from the Democratic Republic of Congo. Vaccine.40(50):732.1–7. DOI: http://dx.doi.org/10.1016/j. vaccine.2022.10.078 Somma S., Akinwande N.,& Chado U. (2019). A mathematical model of monkey pox virus transmission dynamics. IFE J Sci. 21(1):195–204. TeWinkel R. E. (2019). Stability analysis for the equilibria of a monkeypox model. Thesis and Dissertations: University of Wisconsin. https://dc.uwm.edu/etd/2132 Usman S. & Isa Adamu I. (2017). Modeling the Transmission Dynamics of the Monkeypox Virus Infection with Treatment and Vaccination Interventions. Journal of Applied Mathematics and Physics, 5, 2335-2353. DOI: 10.4236/jamp.2017.512191. World Health Organization. Fact sheet: Mpox. Available from: https://www.who.int/news-room/factsheets/detail/monkeypox
PDF