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- Gul Zaman, Yong Han Kang, Il Hyo Jung
- Biosystems
- 2008

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)

- Javed Ali, Saeed Islam, Siraj-ul-Islam, Gul Zaman
- Computers & Mathematics with Applications
- 2010

- Abid Ali Lashari, Gul Zaman
- Computers & Mathematics with Applications
- 2011

- Gul Zaman, Yong Han Kang, Il Hyo Jung
- Biosystems
- 2009

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)

- Gul Zaman
- Comp. Math. Methods in Medicine
- 2011

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)

- Muhammad Altaf Khan, Saeed Islam, Sher Afzal Khan, Gul Zaman
- BioMed research international
- 2013

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)

- Gul Zaman, Yong Han Kang, Hyo Jung
- 2007

Mathematical epidemiological models for the dynamics of infections that induce lifelong immunity have been extensively developed. In this work, we consider a nonlinear SIR model given by a nonlinear system describing the dynamics of the interaction between susceptible and infec-tive individuals in population. We analyze the dynamical behavior of the… (More)

- Abid Ali Lashari, Shaban Aly, Khalid Hattaf, Gul Zaman, Il Hyo Jung, Xue-Zhi Li
- J. Applied Mathematics
- 2012

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)

- Roman Ullah, Gul Zaman, Saeed Islam
- J. Applied Mathematics
- 2012

We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate costeffective control effects for the prevention of transmission of disease. To do… (More)

- Vedat Suat Ertürk, Gul Zaman, Shaher Momani
- Computers & Mathematics with Applications
- 2012