Spatial synchrony in fractional order metapopulation cholera transmission

Abstract

Movement of individuals within metapopulations is characterised by individuals frequenting their home ranges. This not only constitutes memory but also nonlocal property of the resulting system making it plausible to be modelled by Fractional order differential equations. In this paper, we propose a fractional order metapopulation model for transmission of cholera between communities with differing standards of living. Important basic properties of the model such as non-negativity of solutions as well as boundedness are tested. The solutions to the model are shown to exist and the steady state is unique whenever it exists. The model is numerically integrated using the iterative Adams-Bashforth-Mouton method. Our results show that, there is increase synchronous fluctuation in the population of infected individuals in connected communities with either restricted movement or with unrestricted movement of susceptible and infected individuals. In communities with movement restricted to only susceptible individuals, synchronous fluctuation of the infected population in the two communities is more pronounced at lower orders of the fractional derivatives. In unrestricted communities however, the infected population in the two adjacent communities synchronously regardless of the order of the fractional derivative.