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.
Highlights
Like other organisms, oysters require energy to maintain their structure and maturity
The adult oysters produce eggs or sperms before releasing them to fertilize in the water column in the proper environment
After 2–3 weeks, they start to attach to a suitable hard substance, such as rock or shell. They are known as spat and become adult oysters in 1–3 years [1]
Summary
Oysters require energy to maintain their structure and maturity. After 2–3 weeks, they start to attach to a suitable hard substance, such as rock or shell. They are known as spat and become adult oysters in 1–3 years [1]. The Princeton Ocean Model (POM) is widely used to simulate marine circulation [2], and the dynamic energy budget model (DEB) is developed for mechanistic studies [3,4,5,6]. Mortality of bivalve species living in variable environmental conditions has been widely studied due to their ecological and economic importance. Lavaud et al [10] proposed that salinity maintenance may be extracted from struc-
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