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Modeling and optimal control of monkeypox with cost-effective strategies

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Abstract

In this work, we develop and analyze a deterministic mathematical model to investigate the dynamics of monkeypox. We examine the local and global stability of the basic model without control variables. The outcome demonstrates that when the reproduction number \({\mathcal {R}}_{0}<1\), the model’s disease-free equilibrium would be locally and globally asymptotically stable. We further analyze the effective control of monkeypox in a given population by formulating and analyzing an optimal control problem. We extend the basic model to include four control variables, namely preventive strategies for transmission from rodents to humans, prevention of infection from human to human, isolation of infected individuals, and treatment of isolated individuals. We established the necessary conditions for the existence of optimal control using Pontryagin’s maximal principle. To illustrate the impact of different control combinations on the spread of monkeypox, we use the fourth-order Runge–Kutta forward–backward sweep approach to simulate the optimality system. A cost-effectiveness study is conducted to educate the public about the most cost-effective method among various control combinations. The results suggest that, of all the combinations considered in this study, implementing preventive strategies for transmission from rodents to humans is the most economical and effective among all competing strategies.

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Data Availability

Data used to support the findings of this study are included in the article. The authors used a set of parameter values whose sources are from the literature as shown in Table 1.

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Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, University of Medical Sciences, Ondo City, Ondo State, Nigeria

    Olumuyiwa James Peter

  2. Department of Epidemiology and Biostatistics, School of Public Health, University of Medical Sciences, Ondo City, Ondo State, Nigeria

    Olumuyiwa James Peter

  3. Department of Mathematics, Federal University of Agriculture, Makurdi, Benue State, Nigeria

    Chinwendu E. Madubueze

  4. Thermo Fisher Scientific, Microbiology Division, Lenexa, KS, USA

    Mayowa M. Ojo

  5. Department of Mathematical Sciences, University of South Africa, Florida, South Africa

    Mayowa M. Ojo

  6. Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria

    Festus Abiodun Oguntolu

  7. Department of Mathematical Sciences, Osun State University, Osogbo, Osun State, Nigeria

    Tawakalt Abosede Ayoola

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  1. Olumuyiwa James Peter
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  2. Chinwendu E. Madubueze
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  3. Mayowa M. Ojo
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  4. Festus Abiodun Oguntolu
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  5. Tawakalt Abosede Ayoola
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Correspondence to Olumuyiwa James Peter.

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Peter, O.J., Madubueze, C.E., Ojo, M.M. et al. Modeling and optimal control of monkeypox with cost-effective strategies. Model. Earth Syst. Environ. 9, 1989–2007 (2023). https://doi.org/10.1007/s40808-022-01607-z

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