Epidemic metapopulation model on weighted directed networks with pulse movements between nodes

Abstract

In metapopulation disease models, it is generally considered that movements between subpopulations occur in a continuous way. However, there are situations in which this assumption is not fulfilled, as in the case of cattle movements. Here we develop a SIR metapopulation model on weighted directed networks considering that pulse-like movements between subpopulations take place only at certain times, and where each node represents a well-mixed subpopulation. The model is used to analyze the dynamics of the diseases by varying the transmission rates, the time steps for the movements of the individuals through the network, the weight of the links and the network topology. The numerical results indicate that the transmission rate, the time elapsed between movements of individuals and the topology of the network significantly affect the final size of the epidemic. In addition, it can be observed that the network topology drastically affects the disease dynamics within each node. On the other hand, if vaccination is considered in a node, the effectiveness of this control measure depends on the distance between the node where the epidemic begins and the node where the control is applied.