Modeling the dynamics of the consequences of demographic disparities in the transmission of Lassa fever disease in Nigeria

Lassa fever is a zoonotic debilitating disease with huge human and economic loss in the tropics. This work presents a mathematical model describing the transmission of Lassa fever disease in communities with social demographic disparities among the affluent and impoverished humans in the presence of contact tracing, quarantining and hospitalization. The model qualitative results involving the positivity and invariant region of the model are established, while the model’s Lassa fever disease free (LDFE) and Lassa fever endemic equilibrium (LEE) were obtained to show that the LDFE is locally and globally asymptotically stable, whenever the basic reproduction number (Rlassa)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(R_{\mathrm{lassa}})$$\end{document} of the model is less than one, and the LEE is locally asymptotically stable whenever Rlassa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{\mathrm{lassa}}$$\end{document} is greater than one. The graphical illustrations describing the convergence behavior of the model variables when Rlassa<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{\mathrm{lassa}}<1$$\end{document} and Rlassa>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{\mathrm{lassa}}>1$$\end{document} are displayed. In order to describe the dynamics of the disease in Nigeria, data on Lassa fever disease incidence cases for the year 2021 in Nigeria, provided by Nigerian Center for Disease Control is used for the model fitting to obtain the best fit with low residuals. The estimated and fitted parameters of the model were used to perform the sensitivity analysis of model parameters with respect to Rlassa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{\mathrm{lassa}}$$\end{document} and it was found that the positive sensitive values of the recruitment rates of humans and rodents, disease contact rates ψ,βv,βw,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi , \beta _v,\beta _w,$$\end{document} and βz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _z$$\end{document} drives the Lassa fever infection to prevalence. The simulations of the disease contact rates βv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _v$$\end{document} and βw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _w$$\end{document} with respect to Rlassa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{\mathrm{lassa}}$$\end{document} in the human host community, shows that Rlassa>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{lassa}>1$$\end{document}, that is, more humans are infected in the impoverished community compared to affluent community, while Rlassa≈140.009,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{\mathrm{lassa}}\approx 140.009,$$\end{document} shows that approximately 140 humans are being infected weekly on the average in the impoverished human community. These effects calls for strict implementation of controls of sensitization, culling, sanitation etc., to eradicate Lassa fever in Nigeria.