DYNAMIC BEHAVIOUR FOR A NONAUTONOMOUS SMOKING DYNAMICAL MODEL WITH DISTRIBUTED TIME DELAY

Samanta, G.P. The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.3

In this paper we have considered a dynamical mathematical model of the sub-populations of potential smokers (non-smokers), smokers, smokers who temporarily quit smoking, smokers who permanently quit smoking and a class of smoking associated illness by introducing time dependent parameters and distributed time delay to acquire smoking habit. Here, we have established some sufficient conditions on the permanence and extinction of the smoking class in the community by using inequality analytical technique. We have introduced some new threshold values $R_0$ and $R^*$ and further obtained that the smoking class in the community will be permanent when $R_0$ > 1 and the smoking class in the community will be going to extinct when $R^*$ < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

ANALYSIS OF A NONAUTONOMOUS PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE AND TIME DELAY

G. P. Samanta,D. N. Garain 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.3

In this paper we have considered a nonautonomous predatorprey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using inequality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

ANALYSIS OF A NONAUTONOMOUS PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE AND TIME DELAY

Samanta, G.P.,Garain, D.N. The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.3

In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

DYNAMICAL MODEL OF A SINGLE-SPECIES SYSTEM IN A POLLUTED ENVIRONMENT

Samanta, G.P.,Maiti, Alakes 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.1

The effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view. Here we have studied dynamical model of a single-species population-toxicant system. Two cases are studied: constant exogeneous input of toxicant and rapidly fluctuating random exogeneous input of toxicant into the environment. The dynamical behaviour of the system is analyzed by using deterministic linearized technique, Lyapunov method and stochastic linearization on the assumption that exogeneous input of toxicant into the environment behaves like ‘Coloured noise’.

BIOECONOMIC MODELLING OF A THREE-SPECIES FISHERY WITH SWITCHING EFFECT

Samanta, G.P.,Manna, Debasis,Maiti, Alakes 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.12 No.1

This paper aims to study the problem of combined harvesting of a system involving one predator and two prey species fishery in which the predator feeds more intensively on the more abundant species. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equiblibrium case by using Pontryagin's Maximum principle. Dynamic optimization of the harvest policy is also discussed by taking E(t), the combined harvest effort, as a dynamic variable. Biological and bioeconomic interpretations of the results associated with the optimal equilibirum solution are explained. The significance of the constraints required for the existence of an optimal singular control are also given.

DYNAMIC BEHAVIOUR FOR A NONAUTONOMOUS SMOKING DYNAMICAL MODEL WITH DISTRIBUTED TIME DELAY

G. P. Samanta 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.3

In this paper we have considered a dynamical mathematical model of the sub-populations of potential smokers (non-smokers), smokers,smokers who temporarily quit smoking, smokers who permanently quit smoking and a class of smoking associated illness by introducing time dependent parameters and distributed time delay to acquire smoking habit. Here, we have established some sufficient conditions on the permanence and extinction of the smoking class in the community by using inequality analytical technique. We have introduced some new threshold values R_0 and R* and further obtained that the smoking class in the community will be permanent when R_0 > 1 and the smoking class in the community will be going to extinct when R*< 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

Bioeconomic modelling of a three-species fishery with switching effect

G. P. Samanta,Debasis Manna,Alakes Maiti 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.12 No.1-2

Dynamical model of a single-species system in a polluted environment

G. P. Samanta,Alakes Maiti 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-

The effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view. Here we have studied dynamical model of a single-species population-toxicant system. Two cases are studied : constant exogeneous input of toxicant and rapidly fluctuating random exogeneous input of toxicant into the environment. The dynamical behaviour of the system is analyzed by using deterministic linearized technique, Lyapunov method and stochastic linearization on the assumption that exogeneous input of toxicant into the environment behaves like ‘Coloured noise’.

A delay dynamic model for HIV infected immune response

S.P. Bera,A. Maiti,G.P. Samanta 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.5

Human Immune Deficiency Virus (or simply HIV) induces a persistent infection that leads to AIDS causing death in almost every infected individual. As HIV affects the immune system directly by attacking the CD4+ T cells, to exterminate the infection, the natural immune system produces virus-specific cytotoxic T lymphocytes(CTLs) that kills the infected CD4+ T cells. The reduced CD4+ T cell count produce reduced amount of cytokines to stimulate the production of CTLs to fight the invaders that weakens the body immunity succeeding to AIDS. In this paper, we introduce a mathematical model with discrete time-delay to represent this cell dynamics between CD4+ T cells and the CTLs under HIV infection. A modified functional form has been considered to describe the infection mechanism. Characteristics of the system are studied through mathematical analysis. Numerical simulations are carried out to illustrate the analytical findings.

DYNAMICAL BEHAVIOUR OF A DRINKING EPIDEMIC MODEL

Swarnali Sharma,G. P. Samanta 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.5

In this paper we have constructed a mathematical model of alcoholabuse which consists of four compartments corresponding to four populationclasses, namely, moderate and occasional drinkers, heavy drinkers,drinkers in treatment and temporarily recovered class. Basic reproductionnumber R0 has been determined and sensitivity analysis of R0 indicatesthat β1 (the transmission coefficient from moderate and occasional drinkerto heavy drinker) is the most useful parameter for preventing drinkinghabit. Stability analysis of the model is made using the basic reproductionnumber. The model is locally asymptotically stable at disease freeor problem free equilibrium (DFE) E0 when R0 < 1. It is found that,when R0 = 1, a backward bifurcation can occur and when R0 > 1, theendemic equilibrium E becomes stable. Further analysis gives the globalasymptotic stability of DFE under some conditions. Our important analyticalfindings are illustrated through computer simulation. Epidemiologicalimplications of our analytical findings are addressed critically.