Mathematical Analysis of the Effect of Quarantine on the Dynamical Transmission of Monkey Pox

PDF

Published: 2023-11-15

Page: 473-492


M. E. Philemon *

Department of Mathematics and Statistics, Federal University Wukari, P. M. B 1020, Wukari, Taraba State, Nigeria.

I. A. Olopade

Department of Mathematics and Statistics, Federal University Wukari, P. M. B 1020, Wukari, Taraba State, Nigeria.

E. O. Ogbaji

Department of Mathematics and Statistics, Federal University Wukari, P. M. B 1020, Wukari, Taraba State, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

In recent years, monkeypox has emerged as a significant global public health threat, with rising morbidity and mortality rates due to the disease's spread and synergistic effects. Despite recognizing this threat, there has been limited mathematical modelling to understand its progression. To address this, eight new compartmental models were developed, considering factors like quarantine, congenital infection, and various epidemiological aspects. These models were used to analyze disease-free and endemic equilibrium points for stability. The basic reproduction number ( R0 ), was computed, and sensitivity analyses indicated that parameters like effective contact, infection at birth, and recruitment influx are critical. Numerical simulations using MAPLE 18 demonstrated the importance of quarantine in reducing monkeypox transmission. The study concludes that the model with quarantine measures is more effective in controlling disease spread than one without ( R0q < R0 ).

Keywords: Monkey pox, quarantine, basic reproduction number, stability, sensitivity


How to Cite

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. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1894

Downloads

Download data is not yet available.

References

Durski KN, Mc Collum AM, Nukazawa Y, Petersen BW, Reynolds MG, Briand S, et al. Emergence of monkeypox-west and central Africa, 1970-2017. Morbidity and Mortality Weekly Report. 2018;67(10):306.

Jezek ZM, Szczeniowski M, Paluku KM, Mutombo M, Grab B. Human monkeypox: Confusion with chickenpox. Acta Tropica. 1988;45(4):297-307.

Alakanle M, Meons U, Nchinda G, Okeke, M. I. (2020). Monkey pox in nigeria: Infecton biology,epidiomiology, and evolution. Viruses.12 (11), 1257.

Kantele A, Chickering K, Vapalahti O, Rimoin AW. Emerging disease – the monkeypox epidemic in the democratic republic of congo. Clinical Microbiology and Infection. 2016;22(8):658-659.

Nguyen P, Ajisegiri W, Costantino V, Chughtai A, Maclntyre C. Reemergence of human monkeypox and declining population immunity in the context of urbanization, Nigeria. Emergence Infectious Disease. 2021;27(4):1007-1014.

CDC. What you should know about monkeypox; 2003. Available:https:// www. cdc. gov/ poxvi rus/ monke ypox/

Hutson CL, Galllard-Romero N, Carroll DS, Clemmons C, Salzer JS, Nagy T, et al. Transmissibility of the monkeypox virus clades via respiratory transmission: investigation using the prairie dog-monkeypox virus challenge system. 2013;8(2):55488.

Meyer H, Ehmann R, Smith GL. The post-eradication era. Viruses. 2020;12(2):2661-2672.

Peter OJ, Kumar S, Kumari N, Oguntolu FA, Oshinubi K, Musa R. Transmission dynamics of monkeypox virus: A mathematical modelling approach. Modelling Earth Systems and Environment. 2021;1-2.

Bhunu CP, Mushayabasa S. Modelling the transmission dynamics of pox-like infections. AENG International Journal; 2011.

Bhunu C, Garira W, Magombedze G. Mathematical analysis of a two strain HIV/aids model with antiretroviral treatment. Acta Biotheor. 2009;57(3):361-381.

Usman S, Adamu I. Modeling the transmission dynamics of the monkeypox virus infection with treatment and vaccination interventions. Journal of Applied Mathematics and Physics. 2017;5:2335-2353.

Bankuru SV, Kossol S, Hou W, Mahmoudi P, Rychtar J, Taylor D. A game theoretic model of monkeypox to assess vaccination strategies. Peer Journal. 2020;8(9):9272.

Castillo-Chavez Carlos, Baojun S. Dynamical models of tuberculosis and their applications. Maths. BioSci. Eng. 2004;1(2):361-404.

Rimoin AW, Mulembakam PM, Johnston SC, Smith JO, Kinkela TL, Muyembe JJ. Major increase in human monkeypox 30 years after small pox vaccination campaigns cease in the democratic republic of congo. Proceeding of the National Academy of Sciences. 2010;107(37):16262-16267.

Olaniyi S, Gbadamosi B, Olopade IA. Deterministic model for HIV infection dynamics with optimal control strategy using power series method. Journal of the Nigeria Mathematical Society (NMS). 2013;32(4):87-95.

Somma A, Maffei C, Borroni S, Gialdi G, Fossati A. Post traumatic reactions as individual differences: Latent structure analysis of the international trauma questionnaire in Italian trauma-exposed and non-trauma exposed adults. Mediterranean Journal of Clinical Psychology. 2019;7 (1).

Diekmann O, Heesterbeek JA, Robert MG. The construction of next-generation matrices for compartmental epidemic models. Journal of the Royal Society Interface. 2010;7(47):873-885.

Peter O, Viriyapong R, Oguntolu F, Yosyingyong P, Edogbanya H. Stability and optimal control analysis of an scir epidemic model. J Math Comput Sci. 2020;20(1):2722-2753.

Adeniran GA, Olopade IA, Ajao SO, Akinrinmade VA, Aderele OR, Adewale SO. Sensitivity and mathematical analysis of malaria and cholera co-infection. Asian Journal of Pure and Applied Mathematics. 2022;425-452.

Adewale SO, Olopade IA, Ajao SO, Adeniran GA. Mathematical analysis of diarrhea in the presence of vaccine. International Journal of Scientific and Engineering Research. 2015;6(12):396-404.

Akinwumi TO, Olopade IA, Adesanya AO, Alabi MO. A Mathematical Model for the transmission of HIV/AIDS with early treatment. Journal of Advances in Mathematics and Computer Science. 2021;36(5):35-51.

Kumar S, Sharma S, Singh F, Bhatnagar P, Kumari N. A mathematical model for COVID-19 in Italy with possible control strategies. Mathematical Analysis for Transmission of COVID. 2021;101.

Olopade IA, Adewale SO, Mohammed IT, Ajao SO, Oyedemi OT. Mathematical analysis of the role of detection in the dynamical spread of HIV-TB Co-infection. Journal of Advances in Mathematics. 2016;11(10):5715-5740.

Olopade IA, Adesanya AO, Mohammed IT, Afolabi MA, Oladapo AO. Mathematical analysis of the global dynamics of an SVEIR epidemic model with herd immunity. International Journal of Science and Engineering Investigations. (IJSEI). 2017;6(69):141-148.

Olopade AI, Adesanya AO, Akinwumi TO. Mathematical transmission of SEIR epidemic model with natural immunity. Asian Journal of Pure and Applied Mathematics. 2021;3(1):19-29.

Olopade IA, Adewale SO, Muhammed IT, Adeniran GA, Ajao S, Ogunsola AW. Effect of effective contact tracing in curtaining the spread of covid-19. Asian Journal of Research in Biosciences. 2021;3(2):118-134.

Olopade IA, Ajao SO, Adeniran GA, Adamu AK, Adewale SO,Aderele OR. Mathematical transmission of tuberculosis (TB) with detection of infected undetectected. Asian Journal of Research in Medicine and Medical Sciences. 2022;4(1):100-119.

Saimui P, Mondal J, Khajanchi S. A Mathematical model for COVID-19 transmission dynamics with a case study of india. Chaos, solitons & fractal. 2020;140:110173.

Ajao S, Olopade I, Akinwumi T, Adewale S, Adesanya A. Understanding the transmission dynamics and control of HIV infection: A mathematical model approach. Journal of the Nigerian Society of Physical Sciences. 2023;5(2):1389.

Available:https://doi.org/10.46481/jnsps.2023.1389

Cai L, Li Z. Analysis of a simple vector-host epidemic model with direct transmission. Henan, China: Xinyang Normal University Xinyang 46400; 2010.

Kalyan CN, Goud BS, Reddy CR, Ramadan HS, Bajaj M, Ali ZM. Water cycle algorithm optimized type ii fuzzy controller for load frequency control of a multi-area, multi-fuel system with communication time delays. Energies. 2021;14(17):5387.

Victor V, Zaveri A. Sense and sensitivity analysis: Simple post-hoc analysis of bias due to unobserved confounding. Advances in Neural Information Processing Systems. 2020;33:10999-11009.

Grant R, Nguyen LB, Breban R. Modelling human-to-human transmission of monkeypox. Bull World Health Organ. 2020;98(9):638.

Ladnyj ID, Ziegler P, Kima E. A human infection caused by monkeypox virus in basankusu territory, Democratic republic of congo. Bulletin of the World Health Organization. 1972;46(5):593.