Modeling and Analysis of a Single Species Population with Viral Infection in Polluted Environment

Abstract

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.

A dynamical model for epidemic outbursts by begomovirus population clusters

“…However, it is not clear if more simulation detail also would bring more clarity into the description of virus epidemics, as the identification of causes and consequences gets ever more complicated with increasing model complexity. Qualitative non-linear dynamics studies like Meng and Li (2009) and Chauhan and Misra (2012) hint at complicated system dynamics when plant diseases are controlled by different crop control strategies, or combine with environmental pollution, respectively.…”

Sustainability of a system of two competing prey and a predator in polluted environment

“…Ma and Hallam [16] and Hauping and Ma [9] obtained a survival threshold for single and two species, respectively, under the effect of pollution. Chauhan and Mishra [3] studied a single species model under the combined impact of toxicant and infection. Sinha et.al.…”

A single species population model in polluted environment solved by homotopy analysis method

“…Formulation of a single species population model with viral infection in polluted environment is given by Chauhan and Misra [1]. Let H(t) and P (t) be a single species animal population in terrestrial ecosystem and a virus biomass, respectively, at time t. In the absence of virus biomass, the single species population density grows according to a logistic curve.…”

“…Recently few interesting mathematical models with combined e¤ects of disease and toxicant were studied by [10], for completing and prey predator dynamics. The mathematical model by considering the combined e¤ect of both the infection and the toxican through food intake and environment toxicant was studied by [1]. This model is in the form of nonlinear.…”