Simple Model of Spreading of Two Epidemics: Phase Transition and Pattern Formation

Spreading of two different diseases in small world network, with restriction that an individual can be ill only with one disease in the same time, is investigated in the frame of SIRS model. It was found that in the special range of control parameters the presence of the second disease can significantly decrease the number of individuals, who passed the first disease. The speed of propagation of the wave-front of the epidemic is calculated analytically and good agreement with numerical calculation is obtained. The influence of additional long range connections on epidemic spreading and phase transition is investigated. It is found that in special conditions spatio-temporal patterns, in particular spiral waves, can emerge in the system. Small number of additional long-range connections increases the probability of emerging of spiral waves.