Mathematical model and analysis of monkeypox with control strategies

This paper takes into consideration the development and rigorous analysis of a compartmental mathematical model of monkeypox dynamics in the presence of quarantine and isolation compartments. The newly proposed model is governed by 7-dimensional system of ordinary differential equations which describes the monkeypox transmission and spread between the interacting populations of human and rodent. In view of positivity and boundedness of solutions, the model is shown to be mathematically well posed. The control monkeypox reproduction number, R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0$$\end{document}, is obtained using the next generation matrix approach. The threshold quantity is used to investigate the stability analysis of the monkeypox-free equilibrium. Further qualitative analysis suggests that the model undergoes the phenomenon of backward bifurcation in the presence of the fraction of exposed individuals that are quarantined (κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}) whenever R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0$$\end{document} of the model is below unity. By employing center manifold theory, the possibility of ruling out the occurrence of backward bifurcation when κ=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa =0$$\end{document} is shown. The global asymptotic behaviour of the model around the monkeypox-free equilibrium is established using Lyapunov function method. The respective sensitivity index of individual model parameter with respect to R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0$$\end{document} is obtained to gain epidemiological insights into intervention strategies for monkeypox prevention and control. The effects of variation in the effective contact rate of human to human and other key parameters on the disease transmission dynamics under different scenarios are demonstrated quantitatively. The findings of this study show that, we can attain a monkeypox-free state if quarantine and isolation guidelines are carefully followed, as well as preventative measures that minimize the effective contact rates between humans and rodents as well as between rodents and humans during the monkeypox outbreak.