Endogenous and exogenous factors in the dynamics of childhood infectious diseases

The aim of the present research is to estimate and analyze the impact of several exogenous and endogenous factors of host populations that influence the dynamics of childhood infectious diseases. These factors are the dynamics of susceptible population, recruitment to the susceptible population and the migration of infected individuals.;I present the method for estimation of the dynamics of a susceptible population, the recruitment into susceptibility and use of the knowledge about susceptible dynamics to improve the prediction models. I show that the commonly used mass-action relationship between susceptible and infected populations is not valid for measles when the size of the infected population becomes too small. I present an alternative model that is a modification of the mass action model by considering immigration of infected individuals into the host population. I rigorously show that immigration of infectives shifts tangent and period doubling bifurcations to the larger values of periodic forcing in SIR epidemic models and restricts the appearance of subharmonic trajectories in SEIR models.;Although based on measles models and data, the conclusions are applicable to the other host populations and thus can be used in various future studies.