Abstract
We present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local population for a short stay. In particular, the model allows for a constant inflow of individuals into different classes and constant outflow of individuals from the R-class. The system of ordinary differential equations has positive solutions and the infected classes remain above specified threshold levels. The equilibrium points are shown to be asymptotically stable. The utility of the model is demonstrated by way of an application to measles.
Highlights
The fight against infectious diseases presents a major challenge to nations and a huge financial burden for governments
In conventional models with inflow of infected, the immigrants usually become part of the one single population, whereas in our current model we have found a way to quantify the rate of removal of migrants out of the population after a short visit
The new SEIR model with migration was shown in detail to comply to the necessary conventional requirements including positivity and boundedness of solutions, and stability of equilibrium points
Summary
The fight against infectious diseases presents a major challenge to nations and a huge financial burden for governments. In this paper we present a model for quantifying the effects of sporadic migration of infected individuals into and out of a region where there is good control and progress towards elimination. There are numerous papers in the literature that present models for the population dynamics of infectious diseases. This includes models which accommodate the inflow of. This seems to be the first model that provides for recovered migrants to depart from the population at a constant rate In particular this model is meant to be utilised for quantifying the effect of infected migrants on the local population. The constant K4 is the rate of outflow of migrants from the local population, and in particular, moving out of the R-class. The following system of equations is presented as our model
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