Browsing by Author "Adewale, S. O."

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    MATHEMATICAL ANALYSIS FOR DYNAMICAL SPREAD OF MALARIA IN THE POPULATION WITH CONTROLLING MEASURES
    (International Journal of Innovation and Scientific Research, 2017-07) Adewale, S. O.; Omoloye, M. A.; Olopade, I. A.; Adeniran, G. A.
    A system of differential equation approach was used to model the dynamical spread of malaria where humans and vectors interact and infect each other. Positivity of solution showed that there exists a domain where the model is epidemiologically and mathematically well-posed. The basic reproduction number R0 < 1 shows that disease can be controlled in the environment, otherwise the disease persist and become endemic whenever R0 > 1. Also, the numerical analysis performed shows that the most effective strategies for controlling malaria is to reduce the vector biting rate and increased the human treatment.
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    MATHEMATICAL ANALYSIS OF LASSA FEVER MODEL WITH ISOLATION
    (Asian Journal of Natural & Applied Sciences, 2016-09) Adewale, S. O.; Olopade, I. A.; Ajao, S.O.; Adeniran, G. A.; Oyedemi, O. T.
    In this paper, a mathematical model with isolation of infected individuals for the transmission of Lassa fever is developed and analyzed. We obtained the basic reproduction number o R which is the average number of new secondary infection generated by a single infected individual/rat during infectious period. The analysis shows that the disease free equilibrium is locally and globally asymptotically stable whenever the threshold quantity o R is less than unity i.e. R 1 o  . The endemic equilibrium of the model exists under certain condition. The numerical analysis carried out using MAPLE 17 software. The result shows that the isolation of infected individuals reduces the dynamical spread of Lassa as there will be less interaction with the infected individual in the society, the result also shows that treatment of infected-isolated individuals gives a better result which means that government should intensify effort in isolation and the treatment of isolated-infected individuals in order to control the spread of the disease.
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    Mathematical Analysis of Sensitive Parameters on the Dynamical Spread of HIV
    (International Journal of Innovative Research in Science, Engineering and Technology, 2016-05) Adewale, S. O.; Olopade, I. A.; Ajao, S. O.; Mohammed, I. T.
    Sensitivity analysis was performed on a mathematical model of Human Immunodefiency Virus (HIV) to determine the gauge and importance of each parameter to basic reproduction number in the dynamical spread of the disease. The threshold basic reproduction number , 0 R which is the average number of secondary infection generated by infected individuals in his or her infectious period was calculated using next generation matrix method, which shows that, the disease dies out when R0  1, and the disease will persist and spread when 1 0 R  .The relative sensitivity analysis was computed for all the parameters in the basic reproduction number, which shows the influence of each parameter in the dynamical spread of the disease. Numerical sensitivity reveals that effective contact rate and progressor rate are the most sensitive parameters in the basic reproduction number. This analysis will help the medical practitioners and policy health makers to know the best control intervention strategies to be adopted in order to reduce dynamical spread of Human Immunodefiency Virus (HIV) in the community
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    MATHEMATICAL AND SENSITIVITY ANALYSIS OF THE DYNAMICAL SPREAD OF CHOLERA
    (International Journal of Innovation and Applied Studies, 2017-01) Adewale, S. O.; Adeniran, G. A.; Olopade, I. A.; Ajao, S.O.; Mohammed, I. T.
    Sensitivity analysis was performed on the mathematical model of Cholera to determine the influence and importance of each parameter on the basic reproduction number (R0) in the dynamical spread of Cholera. Basic Reproduction Number (R0) was obtained using next generation matrix method (NGM). The disease free equilibrium was analyzed for stability and the analysis shows that the disease free equilibrium point is globally asymptotically stable whenever the basic reproduction number is less than unity i.e (R0<1). Also, there exist endemic equilibrium points of the model whenever R0>1. The relative sensitivity indices of the model with respect to each parameter in the basic reproduction number is calculated in order to find the most sensitive parameter which the medical practitioners and policy health makers should work on in order to reduce the spread of cholera in the society. The result shows that effective contact rate and fraction of individuals with low immunity are the most sensitive parameters in the reproduction number. Numerical simulation was carried out by MAPLE 17 software using Runge-kutta method of order four to show the effects of contact rate and fraction of individuals with low immunity in the dynamical spread of Cholera. This work will allow the health policy makers to know the best control measure to be adopted in order to have disease free environment.
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    Modelling the Effect of DOTS and Isolation on TB Transmission Dynamics
    (IOSR Journal of Mathematics, 2014-04) Adewale, S. O.; Olopade, I. A.; Garba, S.; Olanrewaju, P. O.
    A deterministic model for the transmission dynamics of Tuberculosis (TB) under Direct Observation Therapy Strategy (DOTS) and Isolation in Nigeria is developed and rigorously analysed. The model, consisting of mutually-exclusive epidemiological compartments representing the number of undetected, detected and isolated individuals who are treated under DOTS programme and those who developed Multi-drug resistance. The model has a disease free equilibrium (DFE), which is locally asymptotically stable, whenever the maximum of the associated reproduction numbers of the model (denoted by Rc) is less than unity. Furthermore, the model undergoes a backward bifurcation, where the disease-free equilibrium co-exists with a stable endemic equilibrium. Numerical simulations, using epidemiological and demographic data relevant to Nigeria obtained from WHO and USAID [35,36,38], shows that provided the rate at which the undetected individuals with active TB recovered exceeded a critical values, then DOTS, the STOP TB initiative programme of WHO can lead to effective elimination of TB in Nigeria. This suggest that the detection rate plays significant role in the elimination of TB. Furthermore, it is shown that if the progress or rate of individuals who are susceptible to TB is low, it can also lead to elimination of the disease in Nigeria. The results also shows that if the effective contact rate (  ) for TB infection remains below certain critical value (0.187), the disease can be eliminated.
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    OPTIMAL CONTROL ANALYSIS OF THE DYNAMICAL SPREAD OF MEASLES
    (International Journal of Research - GRANTHAALAYAH, 2016-05) Adewale, S. O.; Olopade, I. A.; Ajao, S.O.; Adeniran, G. A.
    In this paper, a five (5) compartmental model is presented to study the transmission dynamics of Measles in a population at any point in time. The model is rigorously analyzed to gain insight into the dynamical features of Measles and also, optimal control theory is applied to give an optimality system which we used to minimize the number of infected individuals and propose the most suitable control strategy for the spread of measles. It is shown that the model has a diseases free equilibrium which is globally asymptotically stable (GAS). Also, there exists a unique endemic equilibrium point which is locally stable whenever the associated threshold quantity exceeds (one) unity. We also show that there exists a solution for the optimality system. From the result, it was observed that vaccine control strategy is more efficient in reducing the number of infected individuals as compared to other control strategies.