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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

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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

We formulated a mathematical model for the transmission and control of zika virus fever dynamics, incorporating controls; and mosquito bite, sexual contact, vertical transmission blood transfusion as medium of transmissions. Based on our previous findings that the model is mathematically well posed for analysis, the state variables at the endemic state are expressed in terms of parameters and forces of infection, substitution and simplifying led to a polynomial. Invoking Descartes sign rule of polynomial confirmed the existence of a unique endemic equilibrium point of the model if and only if the effective reproduction number is greater than one (1 e R >).