Comparative studies on a zooplankton–fish model subjected to infection in zooplankton with varying rates of disease transmission

Abstract

Eco-epidemiological models offer practical demonstrations of non-linear dynamics, enriching the realm of mathematical biology. The importance of viruses in oceanic plankton ecosystems is becoming more widely acknowledged. Infectious diseases have the potential to significantly alter the interaction within ecological systems. In this article we propose and analyze a three compartmental mathematical model of ODEs involving zooplankton and fish, with SI-type disease in the zooplankton population and two different non-linear infection rates. This study looks at how susceptible zooplankton species behave when in the presence of an infected zooplankton population. We further consider fish population as the sole predator of zooplankton population without considering the specific feeding habits of fish when they consume zooplankton. Additionally, it is thought that the zooplankton population that is infected is more likely to be preyed upon than their non-infected counterparts. The models describe when populations stay constant or show cyclical patterns in behavior. Our research shows that both the systems possess five different biologically feasible steady states. Our study also reveals that the susceptible zooplankton class is adversely impacted by the infection rate. The fish population disappears once the natural mortality rate of fish species surpasses a certain critical value. If the fish population is unable to exceed a certain threshold due to predation of infected zooplankton, they will not survive. For a healthy ecosystem, a lower infection rate and increased fish growth attributed to predation of susceptible zooplankton is preferred. However, an increased rate of infection may cause population collapse in the fish population.