Browsing by Author "Wasike, Adu A.M."

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    A HIV/AIDS model in a homogeneous population with time lags in the transmission
    (HIKARI Ltd: Applied Mathematical Sciences, 2014-01-01) Wasike, Adu A.M.; Kibwott, Frankline T; Lawi, GO; Mulati, Nyukuri Omukoba
    We investigate a simple HIV/AIDS epidemic model in a heterosexual population by by modifying a Susceptible-Infective-Removed (SIR) model. The model considers sexual transmission of HIV where individuals are being recruited into sexually matured age group at a constant rate and incorporates time lags for one to become infective and the other to become fully blown. A complete qualitative analysis of the model, including the boundedness and positivity of the solutions, local stability of the equilibrium points is done. We applly the next generation matrix to determine the disease reproduction number R0. The Model is shown to be completely determined by the reproduction number. The model is numerically analysed to asses the effects of the delay on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Kenya.
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    Stability bifurcation Analysis of a fishery model with nonlinear variation in market price
    (HIKARI Ltd: Applied Mathematical Sciences, 2018-01-01) Makwata, Harun Omukuba; Wasike, Adu A.M.; Chikamai, Lucy W.
    Stability bifurcation Analysis of a fishery model with nonlinear variation in market price We develop a fishery model with price dependent harvesting by formulating a system of three differential equations describing its dynamics. Assuming that the price of the harvested fish on the market evolves relatively faster than the evolution of the fish stock and the fishing effort, we apply approximate aggregation to reduce the system of equations from three to two. From the stability analysis of the aggregated model, we show the co-existence of three strictly positive equilibria where two are stable and are separated by a saddle. The two stable equilibtia rep- resent two kinds of fishery namey; an over-exploited fishery where the fishery supports a large economic activity but risks extinction and an under-exploited fishery where the stock is maintained at a large level far from extinction but the fishery only supports a small economic activity.