Stochastic modeling of the <i>Monkeypox</i> 2022 epidemic with cross-infection hypothesis in a highly disturbed environment

Asad Khan; Yassine Sabbar; Anwarud Din; Asad Khan; Yassine Sabbar; Anwarud Din

doi:10.3934/mbe.2022633

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 13560-13581. doi: 10.3934/mbe.2022633

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Stochastic modeling of the Monkeypox 2022 epidemic with cross-infection hypothesis in a highly disturbed environment

1.
School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
2.
LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
3.
Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
Academic editor: Sanling Yuan

Received: 01 June 2022 Revised: 16 August 2022 Accepted: 25 August 2022 Published: 15 September 2022

Monkeypox 2022, a new re-emerging disease, is caused by the Monkeypox virus. Structurally, this virus is related to the smallpox virus and infects the host in a similar way; however, the symptoms of Monkeypox are more severe. In this research work, a mathematical model for understanding the dynamics of Monkeypox 2022 is suggested that takes into account two modes of transmission: horizontal human dissemination and cross-infection between animals and humans. Due to lack of substantial knowledge about the virus diffusion and the effect of external perturbations, the model is extended to the probabilistic formulation with Lévy jumps. The proposed model is a two block compartmental system that requires the form of Itô-Lévy stochastic differential equations. Based on some assumptions and nonstandard analytical techniques, two principal asymptotic properties are proved: the eradication and continuation in the mean of Monkeypox 2022. The outcomes of the study reveals that the dynamical behavior of the proposed Monkeypox 2022 system is chiefly governed by some parameters that are precisely correlated with the noise intensities. To support the obtained theoretical finding, examples based on numerical simulations and real data are presented at the end of the study. The numerical simulations also exhibit the impact of the innovative adopted mathematical techniques on the findings of this work.
- Monkeypox 2022,
- stochastic analysis,
- extinction,
- persistence,
- numerical simulations
Citation: Asad Khan, Yassine Sabbar, Anwarud Din. Stochastic modeling of the Monkeypox 2022 epidemic with cross-infection hypothesis in a highly disturbed environment[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 13560-13581. doi: 10.3934/mbe.2022633

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Abstract

Monkeypox 2022, a new re-emerging disease, is caused by the Monkeypox virus. Structurally, this virus is related to the smallpox virus and infects the host in a similar way; however, the symptoms of Monkeypox are more severe. In this research work, a mathematical model for understanding the dynamics of Monkeypox 2022 is suggested that takes into account two modes of transmission: horizontal human dissemination and cross-infection between animals and humans. Due to lack of substantial knowledge about the virus diffusion and the effect of external perturbations, the model is extended to the probabilistic formulation with Lévy jumps. The proposed model is a two block compartmental system that requires the form of Itô-Lévy stochastic differential equations. Based on some assumptions and nonstandard analytical techniques, two principal asymptotic properties are proved: the eradication and continuation in the mean of Monkeypox 2022. The outcomes of the study reveals that the dynamical behavior of the proposed Monkeypox 2022 system is chiefly governed by some parameters that are precisely correlated with the noise intensities. To support the obtained theoretical finding, examples based on numerical simulations and real data are presented at the end of the study. The numerical simulations also exhibit the impact of the innovative adopted mathematical techniques on the findings of this work.

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