The relationship between the basic reproduction number R0 and the exponential growth rate, specific to pair approximation models, is derived for the SIS, SIR and SEIR deterministic models without demography. These models are extended by including a random rewiring of susceptible individuals from infectious (and exposed) neighbours. The derived relationship between the exponential growth rate an...

We consider a discrete time model of semelparous biennial population dynamics. Interactions between individuals are modelled with the aid of an "environmental" variable I. The impact on and the sensitivity to the environmental condition is age specific. The main result is that competitive exclusion between the year classes is possible as is their coexistence. For moderate values of the basic re...

In this paper, we studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, R0, is derived. If R0 6 1, the disease-free equilibrium is globally stable and the disease always dies out. If R0 > 1, there exists a unique endemic equilibrium which is locally stable. Furthermore, we proved the global stability of the unique ...

Using a multiple stage age of infection model, we derive an expression for the basic reproduction number, R0. We apply this method to find R0 in analogous treatment models. We find, in the model without treatment, R0 depends only on the mean infective period, and not on the infective distribution. In treatment models, R0 depends on the mean infective and mean treatment period, as well as the di...

Under what circumstances is it morally responsible to procreate with the intention of having children, in view of what parents owe their children? Three conditions are necessary for procreation to be morally responsible: the worthwhile-life condition, the doing-more condition, and the basic-needs condition. The worthwhile-life condition requires that a life be expected to be worth starting in t...

The basic reproduction number $R_{0}$ is a fundamental quantity in epidemiological modeling, reflecting the typical of secondary infections that arise from single infected individual. While widely known to scientists, policymakers, and ...