Browsing by Author "Akinyemi, S. T"
Now showing 1 - 4 of 4
Results Per Page
Sort Options
Item Global Stability Analysis of Sir Epidemic Model with Relapse and Immunity Loss(International Journal of Applied Science and Mathematical Theory ISSN 2489-009X Vol. 2 No.1 2016 www.iiardpub.org, 2016) Akinyemi, S. T; Ibrahim, M. O.; Usman, I. G.; Odetunde, O.A deterministic mathematical model for the transmission dynamics of infectious disease with immunity loss and relapse was built and analyzed. The model was shown to exhibit two equilibria, namely, a disease free equilibrium and an endemic equilibrium. The computated basic reproductive number (R_0) was used to establish that whenever R_0<1, the disease free equilibrium is locally asymptotically stable and the endemic equilibrium is locally asymptotically stable whenever R_0>1. Furthermore the global stability for the two equilibria was investigated using Lyapunov function. The model was simulated numerically to validate the analytical results.Item Mathematical analysis of a staged progression HIV/AIDS model with screening and drug resistance(ABACUS. 43(2) 162 – 179. Published by the Mathematical Association of Nigeria, 2016) Akinyemi, S. T; Ibrahim, M. O.; Moses, M. A.; Edogbanya, H. O.; Odetunde, O.In this paper, a staged progression model for HIV/AIDS transmission dynamics in the presence of screening and drug resistance is developed and rigorously analyzed. The model consist of eight mutually exclusive subpupolations with two equilibria, namely the disease free and endemic equilibrium. The disease free equilibrium is shown to be globally asymptotically stable whenever the effective reproduction number is less than unity by constructing Lyapunov function. Using the Kranoselski sublinearity trick and Lyapunov function, the endemic equilibrium for a special case was establish to be locally and globally asymptotically stable respectively when its associated effective reproduction number exceeds unityItem Mathematical modeling of Hepatitis B transition to primary liver cancer with consideration of partial immunity.(Journal of the Nigerian Association of Mathematical Physics 32 211 – 220. Published by the Nigerian Association of Mathematical Physics., 2015) Odetunde, O.; Ibrahim, M. O.; Lawal, J.; Edogbanya, H. O.; Akinyemi, S. TThis work study the rate of progression of Hepatitis B to Primary Liver Cancer, the effect of therapeutic treatment on the HBV and the role of vaccination of pregnant women as passive immunity for the unborn child. The equilibria states of both the disease free and the endemic were calculated. Positivity of the solution of the model was analyzed and the effective reproduction number was computed. The analysis of the reproduction number at the DFE indicated a substantial decrease in the number of secondary infection rate as a result of passively acquired immunity of the infant and the therapeutic treatment now available to HBV. However, the study show that the rate of progression to primary liver cancer (PLC) will be on the increase if the treatment is not affordable to all HBV patientsItem On the stability analysis of infectious model with therapy(Journal of the Nigerian Association of Mathematical Physics 32, 221 – 228. Published by the Nigerian Association of Mathematical Physics, 2015) Ayoade, A. A.; Ibrahim, M. O.; Edogbanya, H. O; Odetunde, O.; Akinyemi, S. T