| Citation: |
Yandan Zhang, Tailei Zhang, Zhimin Li. A RUBELLA EPIDEMIC MODEL WITH SEASONALITY[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1207-1225. doi: 10.11948/20250104
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A RUBELLA EPIDEMIC MODEL WITH SEASONALITY
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Abstract
In this paper, we formulate a periodic SVPEAIRS model based on the transmission features of rubella. We define the basic reproduction number R0 and show that the disease-free equilibrium is globally asymptotically stable when R0 < 1. The disease is uniformly persistent and there is at least one positive periodic solution when R0>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.
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Keywords:
- Rubella /
- seasonal patterns /
- basic reproduction number /
- threshold dynamics
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References
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Yandan Zhang, Tailei Zhang, Zhimin Li. A RUBELLA EPIDEMIC MODEL WITH SEASONALITY[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1207-1225. doi: 10.11948/20250104
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Figure 1.
Schematic flow diagram for the rubella model (2.1).
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Figure 2.
Comparison of reported cases of rubella in China from January 2012 to December 2018 and model (2.1) simulations, where time 0 represents January 1th, 2012, until December 31th, 2018.
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Figure 3.
When
$ {{\rm{{\cal R}}}_0} = 0.9367 $ -
Figure 4.
When
$ {{\rm{{\cal R}}}_0} = 1.8856 $ -
Figure 5.
When
$ {{\rm{{\cal R}}}_0} = 2.0152 $ -
Figure 6.
Difurcation diagrams.
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Figure 7.
Phase plane diagram.