A RUBELLA EPIDEMIC MODEL WITH SEASONALITY

In this paper, we formulate a periodic SVPEAIRS model based on the transmission features of rubella. We define the basic reproduction number <i>R</i>₀ and show that the disease-free equilibrium is globally asymptotically stable when <i>R</i>₀ &lt; 1. The disease is uniformly persistent and there is at least one positive periodic solution when <i>R</i>₀&gt;1. Numerically, we find that rubella cases in China fluctuate periodically with seasonal changes. Furthermore, when the vaccination rate significantly drops from 0.3 to 0.15, or the recovery rate decreases from 0.6 to 0.3, the rubella epidemic will show an explosive growth trend. This finding emphasizes the great significance of maintaining a high vaccination coverage rate and improving the efficiency of medical treatment in preventing the large-scale spread of rubella. Finally, we analyze the bifurcation phenomenon of the model.