Threshold dynamics in a periodic three-patch rift valley fever virus transmission model

Abstract

This paper investigates a three-patch Rift Valley fever virus transmission model with periodic coefficients. The basic reproduction number Ri0 i = 1,2,3 is calculated for the model by using the next infection operator method. The threshold conditions on the extinction and permanence in the mean of the disease with probability one. The Rift Valley fever disease will be permanent in the j-th j = 1,2,3 patch if j ≥ i, Ri0 > 1 and dies out in the j-th patch if j < i. The numerical simulations are given to confirm the theoretical results.