Abstract
This paper models the spread of an SIR-epidemic with infection age in a heterogeneous complex network and the basic reproduction number is obtained. Next, the accuracy of the main results is confirmed in simulations. Finally, we focus on the impact of infection age on the spread of the disease and show that the recovery time distribution has a significant effect on the disease dynamics. When the recovery time conforms to Uniform distribution or unimodal Gamma distribution, keeping the mean unchanged and increasing the variance will reduce the peak point, the final cumulative epidemic incidence and the basic reproduction number, and will increase the epidemic duration. Furthermore, we show the different effects of different distributions. Compared with the unimodal Gamma distribution with an expectation of 1 and a variance less than 1, the unimodal Weibull distributions with the same expectation and variance bring the greater peaks and the greater cumulative epidemic incidences. Beyond the above facts, we try to explain the reasons behind them.
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