Browsing by Author "Nkansah-Gyekye, Yaw"
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Item Modeling the Effect of Stress and Stigma on the Transmission and Control of Tuberculosis Infection(Technology, and Sciences, 2016) Lengiteng, Lalashe; Kajunguri, Damian; Nkansah-Gyekye, YawIn this paper a continuous time deterministic model with health education campaign and treatment strategy is formulated to assess the effect of stress and stigma on the transmission and control of Tuberculosis (TB). The effective reproduction number eℜis obtained and used to investigate the impact of health education campaign and treatment strategies. The effective reproduction numbers for health education campaign and treatment considered separately were found not to be effective as compared to a combination of both strategies. Numerical simulation results show that TB can be reduced or eliminated from the community when 10<ℜas treatment is applied. The disease prevalence and incidence are high when stigma is high and decline gradually when the combination of both treatment and health campaign are administered. We recommend that health education campaign to reduce stress among individuals and stigma for infectious individuals should be accompanied by treatment of active TB individuals for improved reduction of TB disease.Item Optimal Control Strategies For The Dynamics Of Rift Valley Fever(Communications in Optimization Theory, 2014) Mpeshe, Saul C.; Luboobi, Livingstone S.; Nkansah-Gyekye, YawA model to assess the impact of some control measures in the dynamics of Rift Valley Fever (RVF) is considered. We derived and analysed the conditions for optimal control of RVF with insecticides, vaccination, and personal protection using optimal control theory. We show that the control measures have a very desirable effect for reducing the number of infected individuals and that multiple controls are more effective than single control. Moreover, we show that effective and optimal use of insecticides and personal protection without the use of vaccination is not beneficial if total elimination of the disease is desirable in the community.Item Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community(International Journal of Mathematics and Mathematical Sciences, 2017) Kahuru, Jairos; Luboobi, Livingstone S.; Nkansah-Gyekye, YawTungiasis is a permanent penetration of female sand flea “Tunga penetrans” into the epidermis of its host. It affects human beings and domestic and sylvatic animals. In this paper, we apply optimal control techniques to a Tungiasis controlled mathematical model to determine the optimal control strategy in order to minimize the number of infested humans, infested animals, and sand flea populations. In an attempt to reduce Tungiasis infestation in human population, the control strategies based on personal protection, personal treatment, educational campaign, environmental sanitation, and insecticidal treatments on the affected parts as well as on animal fur are considered. We prove the existence of optimal control problem, determine the necessary conditions for optimality, and then perform numerical simulations. The numerical results showed that the control strategy comprises all five control measures and that which involves the three control measures of insecticide control, insecticidal dusting on animal furs, and environmental hygiene has the significant impact on Tungiasis transmission. Therefore, fighting against Tungiasis infestation in endemic settings, multidimensional control process should be employed in order to achieve the maximum benefits.