In this paper, a mathematical model is proposed to study the effect of pollutant and virus induced disease on single species animal population and its essential mathematical features are analyzed. It is observed that ...In this paper, a mathematical model is proposed to study the effect of pollutant and virus induced disease on single species animal population and its essential mathematical features are analyzed. It is observed that the susceptible population does not vanish when it is only under the effect of infection but in the polluted environment, it can go to extinction. Also, it has been observed that the replication threshold obtained, increases on account of pollutant concentration consequently decreasing the susceptible population. Further persistence results for the proposed model are obtained and the condition for the existence of the Hopf-bifurcation is derived. Finally, numerical simulation in support of analytical results is carried out.展开更多
This paper addresses the problem of determining the optimal promotional policy for a diffusion model in a segment-specific market under the assumption that the additional demand of the new product also improves brand ...This paper addresses the problem of determining the optimal promotional policy for a diffusion model in a segment-specific market under the assumption that the additional demand of the new product also improves brand image in the form of goodwill of the firm.The model is framed with the assumption that the firm uses the mass and differentiated promotion effort for each segment.The differentiated promotional efforts target each market segment independently and the mass promotional effort reaches different segments with a fixed spectrum.We derive the optimal promotional effort policy for each segment using maximumprinciple and also analyze the stability of the dynamical system by constructing a Lyapunov function through the graph theoretic approach.The analysis gives a deep insight into how the promotional effort should be planned by the decision makers keeping in mind the financial constrains without hindering the promotional effort at the end of the planning period.展开更多
文摘In this paper, a mathematical model is proposed to study the effect of pollutant and virus induced disease on single species animal population and its essential mathematical features are analyzed. It is observed that the susceptible population does not vanish when it is only under the effect of infection but in the polluted environment, it can go to extinction. Also, it has been observed that the replication threshold obtained, increases on account of pollutant concentration consequently decreasing the susceptible population. Further persistence results for the proposed model are obtained and the condition for the existence of the Hopf-bifurcation is derived. Finally, numerical simulation in support of analytical results is carried out.
文摘This paper addresses the problem of determining the optimal promotional policy for a diffusion model in a segment-specific market under the assumption that the additional demand of the new product also improves brand image in the form of goodwill of the firm.The model is framed with the assumption that the firm uses the mass and differentiated promotion effort for each segment.The differentiated promotional efforts target each market segment independently and the mass promotional effort reaches different segments with a fixed spectrum.We derive the optimal promotional effort policy for each segment using maximumprinciple and also analyze the stability of the dynamical system by constructing a Lyapunov function through the graph theoretic approach.The analysis gives a deep insight into how the promotional effort should be planned by the decision makers keeping in mind the financial constrains without hindering the promotional effort at the end of the planning period.
