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...

We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations by the migration of infected individuals. We show how susceptible individuals can act collectively to limit the spread of disease during the initial phase o...

Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time d...

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 ...

The basic reproduction number, R(0), a summary measure of the transmission potential of an infectious disease, is estimated from early epidemic growth rate, but a likelihood-based method for the estimation has yet to be developed. The present study corrects the concept of the actual reproduction number, offering a simple framework for estimating R(0) without assuming exponential growth of cases...