Browsing by Author "Ouifki, Rachid"
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Item An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection(De Gruyter Open, 2013) Obaid, Hasim; Ouifki, Rachid; Patidar, Kailash C.We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.Item Modelling the effect of bednet coverage on malaria transmission in South Sudan(Public Library of Science, 2018) Mukhtar, Abdulaziz Y. A.; Munyakazi, Justin B.; Ouifki, Rachid; Clark, Allan E.A campaign for malaria control, using Long Lasting Insecticide Nets (LLINs) was launched in South Sudan in 2009. The success of such a campaign often depends upon adequate available resources and reliable surveillance data which help officials understand existing infections. An optimal allocation of resources for malaria control at a sub-national scale is therefore paramount to the success of efforts to reduce malaria prevalence. In this paper, we extend an existing SIR mathematical model to capture the effect of LLINs on malaria trans- mission. Available data on malaria is utilized to determine realistic parameter values of this model using a Bayesian approach via Markov Chain Monte Carlo (MCMC) methods. Then, we explore the parasite prevalence on a continued rollout of LLINs in three different settings in order to create a sub-national projection of malaria. Further, we calculate the model’s basic reproductive number and study its sensitivity to LLINs’ coverage and its efficacy. From the numerical simulation results, we notice a basic reproduction number, R0 , confirming a substantial increase of incidence cases if no form of intervention takes place in the commu- nity. This work indicates that an effective use of LLINs may reduce R0 and hence malaria transmission. We hope that this study will provide a basis for recommending a scaling-up of the entry point of LLINs’ distribution that targets households in areas at risk of malaria.