Browsing by Author "Mutwiwa, Jacinta M."

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    Mathematical modelling of the role of interference on the transmission dynamics and management of Hiv and Aids
    (2018-09-22) Mutwiwa, Jacinta M.; Nthiiri, Joyce K.; Kwach, O.
    In this paper, a deterministic mathematical model incorporating interference is developed andanalysed to investigate the role of interference on the transmission dynamics and managementof HIV and AIDS. The model is shown to be positively invariant as well as bounded. Theendemic state is shown to exist provided that the reproduction number is greater than unity.Furthermore, by the use of Routh-Hurwitz criterion and suitable Lyapunov functions, theendemic states are shown to be locally and globally asymptotically stable. This implies thatdisease transmission levels can be kept quite low or manageable with minimal deaths at the peaktimes of the re-occurrences. Numerical simulations indicate that minimal interference againstthe disease lowers the rate of infection and enhances the disease management.
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    A seir model for the spread of influenza
    (KIBU, 2019-06-12) Samuel, Apima B.; Mutwiwa, Jacinta M.
    Many acute infectious diseases have been controlled with the help of research and technology in biological and medical fields. However, influenza, which spreads rapidly in the population, remains a cyclical issue, leading to new global pandemics since it has the capability to evolve. In 1918-1919, the Spanish flu killed over 20 million people while the H1N1 flu pandemic in 2009 killed an estimated 284,500 people. In this paper, a Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model is used to describe the spread of influenza, the model is analysed analytically and numerically. The endemic state was shown to exist provided that the reproduction number is greater than unity. Furthermore, by the use of Routh-Hurwitz criterion and suitable Lyapunov functions, the endemic states are shown to be locally and globally asymptotically stable. This implies that disease transmission levels can be kept quite low or manageable with minimal deaths at the peak times of the re-occurrences. Numerical simulations are performed and compared with the analytical results.