Investigation of lassa fever with relapse and saturated incidence rate: mathematical modeling and control

Lassa fever is a virus that primarily affects people in West Africa. In order to investigate Lassa fever with relapse and saturation incidence rate under quarantine measures, this work develops a mathematical model. The presence, uniqueness, and biological viability of solutions in both traditional and fractional operator senses are among the key aspects of the model that we examine. In order to determine the most important factors influencing the spread of Lassa fever, we have calculated equilibrium stage and reproductive number, along with sensitivity analysis using surface plots and PRCC. The effect of certain parameters on the variables is demonstrated via transcritical and flip bifurcation analysis, and global stability is established using the Lyapunov function technique. In addition, we investigated the model’s chaotic behavior and used phase charts to illustrate how the compartments relate to one another. It displays how important parameters affect subclasses. To represent its ongoing memory impact on the Lassa pandemic, solutions are produced using a caputo operator. The results of the analysis show that changes in parameters, namely in ζ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta$$\end{document}, β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}, η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta$$\end{document}, ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu$$\end{document}, ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho$$\end{document}, and Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta$$\end{document}, have a significant impact on the course and management of the disease. While higher quarantine rates successfully stop the spread of infections, increased saturation effects impede transmission. Furthermore, long-term disease care depends on striking a balance between immune loss, recovery, and disease-induced mortality. In order to prevent epidemic breakouts, our findings highlight the significance of focused interventions including immunization, quarantine enforcement, and behavioral changes. The numerical simulations show the actual behavior of the afflicted persons and the true impact of quarantine measures for control purposes, without noticing the effects of relapse and saturated index. The results achieved by decreasing fractional values are superior and converge to the steady state effectively, as demonstrated by the comparison of the obtained results with various values of χ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi$$\end{document}.