A Fractional SEIR Epidemic Model for Spatial and Temporal Spread of Measles in Metapopulations

Abstract

Measles is a higher contagious disease that can spread in a community population depending on the number of people (children) susceptible or infected and also depending on their movement in the community. In this paper we present a fractional SEIR metapopulation system modeling the spread of measles. We restrict ourselves to the dynamics between four distinct cities (patches). We prove that the fractional metapopulation model is well posed (nonnegative solutions) and we provide the condition for the stability of the disease-free equilibrium. Numerical simulations show that infection will be proportional to the size of population in each city, but the disease will die out. This is an expected result since it is well known for measles (Bartlett (1957)) that, in communities which generate insufficient new hosts, the disease will die out.