On the Stability and Equilibrium Points of Multistaged S I ( n )‎ R Epidemic Models

Abstract EN

This paper relies on the concept of next generation matrix defined ad hoc for a newproposed extended SEIR model referred to as S I ( n ) R -model to study its stability.

The model includes n successive stages of infectious subpopulations, each one actingat the exposed subpopulation of the next infectious stage in a cascade global disposalwhere each infectious population acts as the exposed subpopulation of the next infectiousstage.

The model also has internal delays which characterize the time intervals ofthe coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages.

Since the susceptible subpopulation is common, and thenunique, to all the infectious stages, its coupled dynamic action on each of those stagesis modeled with an increasing delay as the infectious stage index increases from 1 to n .

The physical interpretation of the model is that the dynamics of the disease exhibitsdifferent stages in which the infectivity and the mortality rates vary as the individualnumbers go through the process of recovery, each stage with a characteristic averagetime.