Impact of public awareness on haemo-lyphatic and meningo-encepphalitic stage of sleeping sickness using mathematical model approach

Abstract

The parasitic disease known as sleeping sickness, or human African trypanosomiasis, is spread by vectors. Trypanosoma protozoans are the cause of it. Humans contract the parasites through the bites of tsetse flies (glossina), which have taken up the parasites from infected humans or animals. The boundedness and positivity of solutions of the proposed model have been ascertained, and the existence of equilibria has been accessed, which shows that the model consist of two equilibrium, the disease-free equilibrium and endemic equilibrium points. Using the next-generation matrix method, we calculated the control and basic reproduction number. It has been determined that the disease-free equilibrium is locally asymptotically stable if the control reproduction number is less than unity. The findings indicate that the disease-free equilibrium is globally asymptotically stable whenever the control reproduction number is less than one. A unique endemic equilibrium is contained in the model, as evidenced by the determination of the existence of endemic equilibrium. The global asymptotic stability of the endemic equilibrium point has been determined by applying the non-linear Lyapunov function of the Go-Volterra type. The findings indicate that the endemic equilibrium point is globally asymptotically stable when the control reproduction number is greater than one and when both the disease-induced death and the control reproduction number are zero. In a sensitivity analysis section, we found that beta h\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _h$$\end{document}, beta v\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 a are the three most sensitive parameters for increasing the transmission. On the contrary, sigma 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _2$$\end{document} and theta 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _1$$\end{document} are the two most sensitive for reducing the spread., In the numerical simulation section, we were able to see how important is awareness on the dynamics of trypanosomiasis or sleeping sickness, as it is in numerical simulation section, public awareness was simulated to assess its importance in controlling trypanosomiasis or sleeping sickness in the society.