In this paper, a model is proposed to study the impact of awareness on the dynamics of dengue. It is assumed that due to awareness of the disease some susceptible take necessary precautionary measures to protect thems...In this paper, a model is proposed to study the impact of awareness on the dynamics of dengue. It is assumed that due to awareness of the disease some susceptible take necessary precautionary measures to protect themselves from mosquito bite. A threshold is obtained for the stability of the disease-free equilibrium state. The awareness is found to affect the threshold. For the sufficiently large awareness rate, the endemic state does not exist and disease-free state remains globally stable. It is concluded that the increase in the awareness rate decreases the densities of infectious populations of human as well as mosquitoes.展开更多
In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation...In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coexistence of spotted and stripe-like patterns.展开更多
A dynamical model for toxin producing phytoplankton and zooplankton has been formu- lated and analyzed. Due to gestation of prey, a discrete time delay is incorporated in the predator dynamics. The stability of the de...A dynamical model for toxin producing phytoplankton and zooplankton has been formu- lated and analyzed. Due to gestation of prey, a discrete time delay is incorporated in the predator dynamics. The stability of the delay model is discussed and Hopf bifurcation to a periodic orbit is established. Stability and direction of bifurcating periodic orbits are investigated using normal form theory and center manifold arguments. Global existence of periodic orbits is also established. To substantiate analytical findings, numerical simu- lations are performed. The system shows rich dynamic behavior including chaos and limit cycles. The influence of seasonality in intrinsic growth parameter of the phytoplankton population is also investigated. Seasonality leads to complexity in the system.展开更多
A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability an...A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson＇s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.展开更多
文摘In this paper, a model is proposed to study the impact of awareness on the dynamics of dengue. It is assumed that due to awareness of the disease some susceptible take necessary precautionary measures to protect themselves from mosquito bite. A threshold is obtained for the stability of the disease-free equilibrium state. The awareness is found to affect the threshold. For the sufficiently large awareness rate, the endemic state does not exist and disease-free state remains globally stable. It is concluded that the increase in the awareness rate decreases the densities of infectious populations of human as well as mosquitoes.
文摘In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coexistence of spotted and stripe-like patterns.
文摘A dynamical model for toxin producing phytoplankton and zooplankton has been formu- lated and analyzed. Due to gestation of prey, a discrete time delay is incorporated in the predator dynamics. The stability of the delay model is discussed and Hopf bifurcation to a periodic orbit is established. Stability and direction of bifurcating periodic orbits are investigated using normal form theory and center manifold arguments. Global existence of periodic orbits is also established. To substantiate analytical findings, numerical simu- lations are performed. The system shows rich dynamic behavior including chaos and limit cycles. The influence of seasonality in intrinsic growth parameter of the phytoplankton population is also investigated. Seasonality leads to complexity in the system.
文摘A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson＇s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.
