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Papers by swarnali sharma
International Journal of Dynamics and Control, 2015
Differential Equations and Dynamical Systems, 2015
Journal of Applied Mathematics and Computing, 2014
Chaos, Solitons & Fractals, 2015
ABSTRACT
Journal of Nonlinear Dynamics, 2013
We have considered a tumor growth model with the effect of tumor-immune interaction and chemother... more We have considered a tumor growth model with the effect of tumor-immune interaction and chemotherapeutic drug. We have considered two immune components—helper (resting) T-cells which stimulate CTLs and convert them into active (hunting) CTL cells and active (hunting) CTL cells which attack, destroy, or ingest the tumor cells. In our model there are four compartments, namely, tumor cells, active CTL cells, helper T-cells, and chemotherapeutic drug. We have discussed the behaviour of the solutions of our system. The dynamical behaviour of our system by analyzing the existence and stability of the system at various equilibrium points is discussed elaborately. We have set up an optimal control problem relative to the model so as to minimize the number of tumor cells and the chemotherapeutic drug administration. Here we used a quadratic control to quantify this goal and have considered the administration of chemotherapy drug as control to reduce the spread of the disease. The important m...
Journal of Mathematics, 2013
We have discussed the dynamical behaviour of a single-species population model in a polluted envi... more We have discussed the dynamical behaviour of a single-species population model in a polluted environment which describes the effect of toxicants on ecological system. Boundedness, positivity, and stability analysis of the model at various equilibrium points is discussed thoroughly. We have also studied the effect of single discrete delay as well as double discrete delays on the population model. Existence conditions of the Hopf bifurcation for single time delay are investigated. The length of delay preserving the stability is also estimated. The direction and the stability criteria of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. The stability of the model with double time delays is investigated by using the Nyquist criteria. By choosing one of the delays as a bifurcation parameter, the model is found to undergo a Hopf bifurcation. Some numerical simulations for justifying the theoretical results are also illustrated by using MATLAB, which shows the reliability of our model from the practical point of view.
International Journal of Dynamics and Control, 2014
ABSTRACT
International Journal of Dynamics and Control, 2015
Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Ber... more Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Berlin Heidelberg. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
International Journal of Biomathematics, 2015
In this paper, we have developed a compartment of epidemic model with vaccination. We have divide... more In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0 when R0 < 1. When R0 > 1 endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numeri...
Journal of Biological Systems, 2014
In this paper, we have developed a five-compartmental epidemic model with Chlamydia infection. We... more In this paper, we have developed a five-compartmental epidemic model with Chlamydia infection. We have divided the total population into five classes, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase and recovered class. The basic reproduction number (R0) is calculated using the next-generation matrix method. The stability analysis of the model shows that the system is locally asymptotically stable at the disease-free equilibrium (DFE) E0 when R0 < 1. When R0 > 1, an endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the Chlamydia epidemic model with two treatment controls. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of treatment. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated t...
Nonlinear Dynamics, 2014
ABSTRACT
Nonlinear Dynamics, 2014
ABSTRACT
International Journal of Dynamics and Control, 2015
Differential Equations and Dynamical Systems, 2015
Journal of Applied Mathematics and Computing, 2014
Chaos, Solitons & Fractals, 2015
ABSTRACT
Journal of Nonlinear Dynamics, 2013
We have considered a tumor growth model with the effect of tumor-immune interaction and chemother... more We have considered a tumor growth model with the effect of tumor-immune interaction and chemotherapeutic drug. We have considered two immune components—helper (resting) T-cells which stimulate CTLs and convert them into active (hunting) CTL cells and active (hunting) CTL cells which attack, destroy, or ingest the tumor cells. In our model there are four compartments, namely, tumor cells, active CTL cells, helper T-cells, and chemotherapeutic drug. We have discussed the behaviour of the solutions of our system. The dynamical behaviour of our system by analyzing the existence and stability of the system at various equilibrium points is discussed elaborately. We have set up an optimal control problem relative to the model so as to minimize the number of tumor cells and the chemotherapeutic drug administration. Here we used a quadratic control to quantify this goal and have considered the administration of chemotherapy drug as control to reduce the spread of the disease. The important m...
Journal of Mathematics, 2013
We have discussed the dynamical behaviour of a single-species population model in a polluted envi... more We have discussed the dynamical behaviour of a single-species population model in a polluted environment which describes the effect of toxicants on ecological system. Boundedness, positivity, and stability analysis of the model at various equilibrium points is discussed thoroughly. We have also studied the effect of single discrete delay as well as double discrete delays on the population model. Existence conditions of the Hopf bifurcation for single time delay are investigated. The length of delay preserving the stability is also estimated. The direction and the stability criteria of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. The stability of the model with double time delays is investigated by using the Nyquist criteria. By choosing one of the delays as a bifurcation parameter, the model is found to undergo a Hopf bifurcation. Some numerical simulations for justifying the theoretical results are also illustrated by using MATLAB, which shows the reliability of our model from the practical point of view.
International Journal of Dynamics and Control, 2014
ABSTRACT
International Journal of Dynamics and Control, 2015
Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Ber... more Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Berlin Heidelberg. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
International Journal of Biomathematics, 2015
In this paper, we have developed a compartment of epidemic model with vaccination. We have divide... more In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0 when R0 < 1. When R0 > 1 endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numeri...
Journal of Biological Systems, 2014
In this paper, we have developed a five-compartmental epidemic model with Chlamydia infection. We... more In this paper, we have developed a five-compartmental epidemic model with Chlamydia infection. We have divided the total population into five classes, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase and recovered class. The basic reproduction number (R0) is calculated using the next-generation matrix method. The stability analysis of the model shows that the system is locally asymptotically stable at the disease-free equilibrium (DFE) E0 when R0 < 1. When R0 > 1, an endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the Chlamydia epidemic model with two treatment controls. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of treatment. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated t...
Nonlinear Dynamics, 2014
ABSTRACT
Nonlinear Dynamics, 2014
ABSTRACT