Epidemic transmission on random mobile network with diverse infection periods

•We construct a new epidemic model with diverse infection periods.•The epidemic threshold is obtained by a novel process.•Shorter individual’s infection period leads to larger epidemic threshold.•The homogeneity of individuals will avail to the spreading of epidemics. The heterogeneity of individual susceptibility and infectivity and time-varying topological structure are two realistic factors when we study epidemics on complex networks. Current research results have shown that the heterogeneity of individual susceptibility and infectivity can increase the epidemic threshold in a random mobile dynamical network with the same infection period. In this paper, we will focus on random mobile dynamical networks with diverse infection periods due to people’s different constitutions and external circumstances. Theoretical results indicate that the epidemic threshold of the random mobile network with diverse infection periods is larger than the counterpart with the same infection period. Moreover, the heterogeneity of individual susceptibility and infectivity can play a significant impact on disease transmission. In particular, the homogeneity of individuals will avail to the spreading of epidemics. Numerical examples verify further our theoretical results very well.