Spreading of periodic diseases and synchronization phenomena on networks

In this paper, we investigate numerically the Susceptible–Infected–Recovered–Susceptible (SIRS) epidemic model on an exponential network generated by a preferential attachment procedure. The discrete SIRS model considers two main parameters: the duration τ0 of the complete infection–recovery cycle and the duration τI of infection. A permanent source of infection I0 has also been introduced in order to avoid the vanishing of the disease in the SIRS model. The fraction of infected agents is found to oscillate with a period T≥τ0. Simulations reveal that the average fraction of infected agents depends on I0 and τI/τ0. A maximum of synchronization of infected agents, i.e. a maximum amplitude of periodic spreading oscillations, is found to occur when the ratio τI/τ0 is slightly smaller than 1/2. The model is in agreement with the general observation that an outbreak corresponds to high τI/τ0 values.