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Almost all mathematical models of diseases start from the same basic premise: the population can be subdivided into a set of distinct classes dependent upon experience with respect to the relevant disease. Most of these models classify individuals as either a susceptible individual S, infected individual I or recovered individual R. This is called the… (More)

We present the optimal campaigns in the smoking dynamics. Assuming that the giving up smoking model is described by the simplified PLSQ (potential-light-smoker-quit smoker) model, we consider two possible control variables in the form of education and treatment campaigns oriented to decrease the attitude towards smoking. In order to do this we minimize the… (More)

In this paper the optimal control strategies of an SIR (susceptible-infected-recovered) epidemic model with time delay are introduced. In order to do this, we consider an optimally controlled SIR epidemic model with time delay where a control means treatment for infectious hosts. We use optimal control approach to minimize the probability that the infected… (More)

The paper presents the vector-host disease with a variability in population. We assume, the disease is fatal and for some cases the infected individuals become susceptible. We first show the local and global stability of the disease-free equilibrium, for the case when R 0 < 1. We also show that for R 0 < 1, the disease free-equilibrium of the model is both… (More)

An existing model is extended to assess the impact of some antimalaria control measures, by re-formulating the model as an optimal control problem. This paper investigates the fundamental role of three type of controls, personal protection, treatment, and mosquito reduction strategies in controlling the malaria. We work in the nonlinear optimal control… (More)

- Muhammad Altaf Khan, Murad Ullah, Sher Afzal Khan, G. Zaman, Muhammad Arif, Syed Farasat Sadiq +1 other
- 2013

In this paper, we consider an epidemic model of vector host with non-linear incidences. The spread of the disease is due to the vector such as malaria, dengue and yellow fever. We use the homotopy perturbation method to the consider model to obtain their analytical and numerical solution. Due to the importance of homotopy method a just few perturbation… (More)