Sudipa Chauhan

Effect of pollution on dynamics of SIR model with treatment

In this paper, an SIR epidemic model with treatment affected by pollution is proposed. The existence, local and global dynamics of the model are studied. It is shown that backward bifurcation occurs at R0 1. Further, there exist bistable endemic equilibria for a very low capacity for R0 > 1. Thus, we found that disease can be eradicated for R0 < 1 only by increasing the capacity to a sufficiently high level. Persistence of endemicity of the system is obtained and the mathematical results suggest that the basic reproduction number is insufficient for disease eradication. Numerical simulations are presented to illustrate the results obtained.

Dynamics of Sirs Model with Single Time Delay

In this paper, we have considered two models: SICRS model without and with single time delay in infective population. The global dynamics of both models have been carried out and the effect of carriers on transmission dynamics is discussed through the basic reproduction number.

A Stage-Structured Prey-Predator Fishery Model In The Presence Of Toxicity With Taxation As A Control Parameter of Harvesting Effort

In this paper we have considered stage-structured fishery model in the presence of toxicity, which is diminishing due to the current excessive use of fishing efforts resulting in devastating consequences. The purpose of this study is to propose a bio-economic mathematical model by introducing taxes to the profit per unit biomass of the harvested fish of each species with the intention of controlling fishing efforts in the presence of toxicity. We obtained both boundary and interior equilibrium points along with the conditions ensuring their validity. Local stability for the interior equilibrium point has been found by the trace-determinant criterion and global stability has been analyzed through a suitable Lyapunov function. We have also obtained the optimal harvesting policy with the help of Pontryagins maximum principle. Lastly, numerical simulation with the help of MATLAB have been done and thus, the results of the formulated model have been established.

Sirs Model with Double Time Delay

This paper is concerned with the study of two SIRS Model with Double Time Delay by incorporating time delay in both infective and recovered class. In model I, we have obtained the existence of disease free and endemic equilibrium points. For Model I, by analyzing the eigenvalues of associated characteristic equation of system, the conditions ensuring the local stability of the equilibrium points are obtained. Further, for the Model II the dynamical behavior of the endemic equilibrium is shown from the point of view of stability switches aspects. Finally, numerical simulations have been carried out in support of our result.

Role of delay and screening in controlling AIDS

We propose a non-linear HIV/ AIDS model to analyse the spread and control of HIV/AIDS. The population is divided into three classes, susceptible, infective and AIDS patients. The model is developed under the assumptions of vertical transmission and time delay in infective class. Time delay is also included to show sexual maturity period of infected newborns. We study dynamics of the model and obtain the reproduction number. Now to control the epidemic, we study the model where aware infective class is also added, i.e., people are made aware of their medical status by way of screening. To make the model more realistic, we consider the situation where aware infective class also interacts with other people. The model is analysed qualitatively by stability theory of ODE. Stability analysis of both disease-free and endemic equilibrium is studied based on reproduction number. Also, it is proved that if (R0)1, R1 ≤ 1 then, disease free equilibrium point is locally asymptotically stable and if (R0)1, R1 > 1 then,...

Effect of Holling type-II function on dynamics of discrete prey-predator system with scavenger

A discrete prey predator model with scavengers is proposed. The model is build up by the interaction between three species prey predators and scavengers using difference equation. The stability analysis for the boundary fixed points is carried out showing the survival of prey population and prey-predator population both in the presence of scavenger.