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We show the erroneous assumptions and reasoning by introducing the migration effect of individuals in the transmission model of Hepatitis B virus. First, some false results related to the eigenvalues and reproductive number in the recent literature in mathematical biology will be presented. Then, it will be proved that the product of the matrices in the… (More)

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

- 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)

- 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)

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

- 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)

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

In this work, we solve multipoint boundary value problems using the Optimal Homotopy Asymptotic Method (OHAM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. This method provides easy tools to control the convergence region of approximating solution series where ever… (More)

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

ABSTRACT 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 infective 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

1 Center for Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad 44000, Pakistan 2 Department of Mathematics, Faculty of Science, King Khalid University, Abha 9004, Saudi Arabia 3 Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511, Egypt 4 Department of Mathematics and Computer Science,… (More)