Bioeconomics fishery model in presence of infection: Sustainability and demand-price perspectives

Intense harvesting and emerging infectious diseases are potential threats to global fishery. A proper management policy equipped with the scientific understanding of species interaction is a footstep in a long-term sustainable fishery. This work performs a qualitative study of bioeconomic management of a fishery in presence of some infection. The model narrates the rate equations of the healthy fish, infected fish, fishing effort and market price, where the fishing effort is considered to be dependent on the fish price and the fish price is regulated by the demand-supply theory of the open market. Routh–Hurwitz criterion is utilized for the local stability analysis whereas the high-dimensional Bendixson criterion is used for the global stability analysis. The one and two parameters bifurcation analysis explain various switching in equilibrium states, which includes infection-free, infected and harvesting-free states. The existence conditions of the bionomic equilibrium, where both the ecological and economic equilibrium exists, has been established. The harvested fish biomass is observed to be higher at the infection-free equilibrium state compare to the infected equilibrium state under increasing infection rate, however, the outcome is opposite under increasing environmental carrying capacity. Though, the total revenue is highest at the infection-free state when demand is high. An unintuitive result is that the infection persists at a higher level if demand decreases.