"It's a matter of whether we're going to have a healthy recovered population or isolated animals that are always struggling to survive," said Suzanne Stone, the Northern Rockies representative for Defenders of Wildlife, one of the parties seeking the injunction.
In such a case, the convergence of the recovered population to zero is also at an exponential rate.
An alternative condition for a convergence to zero of the recovered population, perhaps at a rate slower than exponential, is the convergence to zero of the function (5.13).
Here, (a, b, c, d, (geq0)) denote the level of prevention of susceptible individuals, infected individuals, lurkers, and recovered population, respectively.
Let (S^{(1)}_{k}), (S^{(2)}_{k}), (E_{k}), (I_{k}) and (R_{k}) denote the immature susceptible, mature susceptible, infected but non-infectious, infectious and recovered population in the kth group, respectively.
When Oxitec stops its releases, mosquito numbers will rebound, and it is not clear whether or how the genes from the release strain would influence the recovered population, including how mosquitos seek out hosts, mate, or lay eggs, for example.
The disease propagation is described by a SIRS (susceptible plus infected plus recovered populations) epidemic model.
However, the control parameters choice also has to guarantee the positivity of the susceptible, infected and recovered populations for all time as the nature of the system requires.
where, and are, respectively, the susceptible, vaccinated, exposed, infected (or infective or infectious), and recovered populations, is the total population being the sum of the above ones, and is a constant vaccination action.
Thus, there is at least one endemic equilibrium point at which the susceptible, vaccinated, infected, exposed, and recovered populations are positive and the vaccinated population is zero if and only if (i.e., in the absence of vaccination action).
In this paper we propose a new model for infectious diseases spread having susceptible, infected, and recovered populations and study its dynamics in presence of incubation delays and relapse of the disease.
