In this paper, we formulated a mathematical model of the dynamics of Ebola virus infection incorporating effectiveness of drug usage. The infection free and infection persistence equilibrium points were obtained. The control reproduction number was obtained which was used to analyse the local and global stability of the infectionfree equilibrium. Using the method of linearization, the infection-free equilibrium (IFE) state was found to be locally asymptotically stable if R < 1 and unstable if R > 1. By constructing lyapunov function, the infection-free equilibrium was found to be globally asymptotically unstable if R > 1. Numerical simulation of the model was done. It is observed that, as percentage of effectiveness of drug administration increases, the control reproduction number decreases. This suggests that with the help of drugs usage, the immunes system have the ability to suppress the increase of infected cells, as well as virus load which shown that the virus does not maintain an infection in the system.

An infection age structured mathematical model for tuberculosis disease dynamics is investigated in this paper. The infectious population is structured according to time and age of infection. An explicit formula for the basic reproductive number, 0 R of the model is obtained. We showed that the disease-free equilibrium (DFE) state is locally asymptotically stable if 0 1 R  and unstable if otherwise. This simply means that tuberculosis could be controlled in a population when the basic reproduction number is less than unity. © JASEM

In this paper we modified the MSIR Model by adding the vaccination rate and death rate due to the disease to the existing MSIR model. We verified the positivity of the solution and obtained the Disease Free Equilibrium (DFE) of the model. We also determined the basic reproduction number using next generation Matrix and Jacobian matrix methods.

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ABSTRACT:In this work, we propose a Deterministic Mathematical Model that Combines Infectious but not Blind and Infectious Blind Compartments for Onchocerciasis Transmission and Control. Onchocerciasis is usually the term used to describe river blindness, it is a disease that causes blindness, and the second largest cause of blindness after trachoma. It mainly affects the eyes and the skin. The equilibrium states of the model are obtained. The disease free equilibrium state is analysed for stability; the condition for its stability is obtained as an inequality constraint on the parameters. Results shows that although, a 60% treatment coverage rate of infected and infectious blind individuals only is better than 80% treatment coverage rate of infected but not blind individuals only. Also, all the four control strategies reduce the effective reproduction number below unity. A 40% coverage rate of fumigation and treatment of infectious but not blind is better than a 40%coverage rate of fumigation only. It further reveals that a 30% coverage rate of fumigation and treatment of infectious blind is better than 80%coverage rate of fumigation only or fumigation and treatment of infected but not blind only. We are able to show that disease free equilibrium and endemic equilibrium exists and are both locally and globally stable, and we computed the c R of the model and showed that it is a parameter to test for stability, we also use the Jacobi stability technique to show that disease free equilibrium and endemic equilibrium are both locally and globally stable. The sensitivity analysis results shows that the most sensitive parameter is ρ while the least sensitive is v µ , © JASEM https://dx.doi.org/10.4314/jasem.v21i4.6