https://doi.org/10.1140/epjs/s11734-024-01283-3
Regular Article
Complex dynamics of a fractional-order monkeypox transmission system with saturated recovery function
1
Department of Mathematics, Indian Institute of Engineering Science and Technology, 711103, Howrah, West Bengal, India
2
Department of Mathematics, Ramsaday College, 711401, Howrah, West Bengal, India
3
Department of Mathematics, Indian Institute of Technology Guwahati, 781039, Guwahati, Assam, India
Received:
10
May
2024
Accepted:
1
August
2024
Published online:
27
August
2024
Every country is continuously experiencing the monkeypox disease that started in the United Kingdom in May 2022. A detailed understanding of the transmission mechanism is required for controlling the disease. Based on real needs, we have developed an eight-compartmental mathematical model using a system of fractional-order differential equations to understand the behavior of the disease. The fractional-order model is adopted to discuss the effect of memory in reducing monkeypox infection. The next-generation matrix method determines the basic reproduction number for human beings and beasts, which are 
and 
, respectively. Depending on the numerical values of 
and , the feasibility and the nature of the equilibrium points are studied. It is found that the system exhibits two transcritical bifurcations; one occurs at 
for any value of , and the other occurs at 
when 
. The effectiveness of the parameters has been discussed with the help of global sensitivity analysis. Further, we have investigated the optimal control policies, considering vaccination and treatment as two dynamic control variables. The incremental cost-effectiveness ratio and the infected averted ratio are determined to assess the cost-effectiveness of all practical control strategies. From the fractional-order optimal control problem, we have experienced that simultaneous use of both treatment and vaccination controls gives better results than using any single control in reducing infected humans. The global sensitivity analysis shows that controlling certain system parameters can regulate monkeypox infection. Further, our cost-effectiveness analysis shows that treatment control is the most cost-effective method for the monkeypox virus.
Snehasis Barman, Soovoojeet Jana, Suvankar Majee, Anupam Khatua and Tapan Kumar Kar have contributed equally to this work.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
