Modeling the spatial spread of Rift Valley fever in Egypt

Abstract

Rift Valley fever (RVF) is a severe viral zoonosis in Africa and the Middle East that harms both human health and livestock production. It is believed that RVF in Egypt has been repeatedly introduced by the importation of infected animals from Sudan. In this paper, we propose a three-patch model for the process by which animals enter Egypt from Sudan, are moved up the Nile, and then consumed at population centers. The basic reproduction number for each patch is introduced and then the threshold dynamics of the model are established. We simulate an interesting scenario showing a possible explanation of the observed phenomenon of the geographic spread of RVF in Egypt.

Fig. 1

The curves of the basic reproduction number of patch i, ${\mathcal{R}}_{i0}$, versus c

Fig. 2

Numerical simulations of system (2a) showing I_i vs. t. Initial conditions: S₁(0) = 1800, I₁(0) = 50, R₁(0) = 100, V₁(0) = 0, and S₂(0) = I₂(0) = R₂(0) = V₂(0) = S₃(0) = I₃(0) = R₃(0) = V₃(0) = 0. ${\mathcal{R}}_{10}<1$, ${\mathcal{R}}_{20}>1$, and ${\mathcal{R}}_{30}>1$

Fig. 3

Numerical simulations of system (2a) showing V_i vs. t. Initial conditions: S₁(0) = 1800, I₁(0) = 50, R₁(0) = 100, V₁(0) = 0, and S₂(0) = I₂(0) = R₂(0) = V₂(0) = S₃(0) = I₃(0) = R₃(0) = V₃(0) = 0. ${\mathcal{R}}_{10}<1$, ${\mathcal{R}}_{20}>1$, and ${\mathcal{R}}_{30}>1$