Modelling the impact of vaccination and environmental transmission on the dynamics of monkeypox virus under Caputo operator

Emmanuel Addai; Mercy Ngungu; Musibau Abayomi Omoloye; Edmore Marinda; Emmanuel Addai; Mercy Ngungu; Musibau Abayomi Omoloye; Edmore Marinda

doi:10.3934/mbe.2023446

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 10174-10199. doi: 10.3934/mbe.2023446

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Modelling the impact of vaccination and environmental transmission on the dynamics of monkeypox virus under Caputo operator

1.
College of Biomedical Engineering, Taiyuan University of Technology, Shanxi Taiyuan 030024, China
2.
Department of Mathematics, Taiyuan University of Technology, Shanxi Taiyuan 030024, China
3.
Human Sciences Research Council (HSRC), South Africa
4.
Department of Mathematics and Computer Science, Elizade University, Ilara-Mokin, Ondo State, Nigeria

Academic Editor: Xueying Wang

Received: 11 January 2023 Revised: 19 March 2023 Accepted: 21 March 2023 Published: 29 March 2023

In this study, we examine the impact of vaccination and environmental transmission on the dynamics of the monkeypox. We formulate and analyze a mathematical model for the dynamics of monkeypox virus transmission under Caputo fractional order. We obtain the basic reproduction number, the conditions for the local and global asymptotic stability for the disease-free equilibrium of the model. Under the Caputo fractional order, existence and uniqueness solutions have been determined using fixed point theorem. Numerical trajectories are obtained. Furthermore, we explored some of the sensitive parameters impact. Based on the trajectories, we hypothesised that the memory index or fractional order could use to control the Monkeypox virus transmission dynamics. We observed that if the proper vaccination is administrated, public health education is given, and practice like personal hygiene and proper disinfection spray, the infected individuals decreases.
- Caputo fractional derivative,
- reproduction number,
- global asymptotic stability,
- numerical scheme
Citation: Emmanuel Addai, Mercy Ngungu, Musibau Abayomi Omoloye, Edmore Marinda. Modelling the impact of vaccination and environmental transmission on the dynamics of monkeypox virus under Caputo operator[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10174-10199. doi: 10.3934/mbe.2023446

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Abstract

In this study, we examine the impact of vaccination and environmental transmission on the dynamics of the monkeypox. We formulate and analyze a mathematical model for the dynamics of monkeypox virus transmission under Caputo fractional order. We obtain the basic reproduction number, the conditions for the local and global asymptotic stability for the disease-free equilibrium of the model. Under the Caputo fractional order, existence and uniqueness solutions have been determined using fixed point theorem. Numerical trajectories are obtained. Furthermore, we explored some of the sensitive parameters impact. Based on the trajectories, we hypothesised that the memory index or fractional order could use to control the Monkeypox virus transmission dynamics. We observed that if the proper vaccination is administrated, public health education is given, and practice like personal hygiene and proper disinfection spray, the infected individuals decreases.

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