Control strategies for a stochastic model of host–parasite interaction in a seasonal environment

A Within-Host Stochastic Model for Nematode Infection

“…Our work in this paper is directly related to that in [20], where we examine stochastic models for the parasite load of a single host and where the interest is in analysing the efficacy of various grazing management strategies. In [20], we defined control strategies based on isolation and treatment of the host at a certain age t 0 .…”

“…In [20], we defined control strategies based on isolation and treatment of the host at a certain age t 0 . This means that the host is free living in a seasonal environment, and it is transferred to an uninfected area at age t 0 .…”

“…In the uninfected area, the host does not acquire new parasites, undergoes an anthelmintic treatment to decrease the parasite load and varies in its susceptibility to parasite-induced mortality and natural (no parasite-induced) mortality. From a mathematical point of view, an important feature of the analysis in [20] is that the underlying processes, recording the number of parasites infesting the host at an arbitrary time t, can be thought of as age-dependent versions of a pure birth process with killing and a pure death process with killing, which are both defined on a finite state space.…”

“…Here, we complement the treatment of control strategies applied to GI nematode burden that we started in [20] by focusing on strategies that are not based on isolation of the host; to be concrete, our interest is in three grazing strategies that reflect the use of a paddock with safe pasture and/or the efficacy of an anthelmintic drug. Seasonal fluctuations in the acquisition of parasites, the death of parasites within the host and the natural and parasite-induced host mortality are incorporated into our model by using nonhomogeneous Poisson processes.…”

“…Seasonal fluctuations in the acquisition of parasites, the death of parasites within the host and the natural and parasite-induced host mortality are incorporated into our model by using nonhomogeneous Poisson processes. Contrary to [20], grazing management strategies considered in this work lead to, instead of pure birth/death processes with killing, the analysis of several age-dependent birth and death processes with killing. The efficacy and cost of each grazing strategy are defined in terms of the transient probabilities of each of the underlying stochastic processes; that is, the probability that the parasite load of the infected host is at any given level at each time instant, given that a particular control strategy has been applied at the intervention instant t 0 .…”