Host-pathogen interaction for larvae oysters with salinity dependent transmission

Abstract

Mathematical models of host-pathogen interactions are proposed and analyzed. Here hosts are oyster population in a free-swimming larval stage and assumably live in the closed homogeneous environment. In terms of an epidemic, they are classified into two states, namely susceptible and infectious hosts. The epidemic model of oyster hosts with seasonal forced transmission is firstly described by the SIS model where the region of attraction, the existence of equilibrium points, their stability conditions, and upper and lower bounds on the attack rate are investigated. Then free-living pathogen is introduced in the oyster area. Numerical simulations are finally carried out by making use of the various salinity-dependent transmissions in support of the hypothesis that the lower the salinity level, the lower oyster’s immunity.