This study aims to investigate temporal changes in the transmission dynamics of the COVID-19 epidemic and to examine how these changes are associated with government intervention periods. For this purpose, a normalized dynamic SIR model is considered in which the recovery rate, $ \gamma $, is set to $ 1/14 $ day-1 in the primary analysis, while the transmission rate, $ \beta $, is allowed to vary across the periods identified in the analysis rather than being assumed constant. Changes in the case series are identified using change-point analysis, and the resulting model is solved using the Taylor collocation method. The estimated transmission rates are compared across the full-closure, partial-closure, and gradual-normalization periods using non-parametric statistical methods. The Kruskal–Wallis test revealed a statistically significant overall difference in the estimated transmission rates among the three intervention groups ($ H(2) = 14.353 $, $ p = 0.001 $). Subsequent pairwise comparisons using Dunn's post-hoc test with Bonferroni correction indicated significant differences between the full-closure and partial-closure periods and between the full-closure and gradual-normalization periods, whereas the difference between the partial-closure and gradual-normalization periods was not statistically significant. Sensitivity analyses using alternative recovery-rate assumptions ($ \gamma = 1/10 $ and $ \gamma = 1/20 $) yielded the same inferential pattern. These findings indicate that the estimated transmission rates varied across the intervention periods and illustrate the potential of the proposed dynamic SIR framework for characterizing temporal transmission patterns under changing intervention conditions.
Citation: Serpil Ünal, Elçin Çelik, Deniz Uçar. A dynamic SIR epidemic model with the Taylor collocation method: Analysis of transmission dynamics under intervention changes[J]. AIMS Mathematics, 2026, 11(11): 36379-36408. doi: 10.3934/math.20261408
This study aims to investigate temporal changes in the transmission dynamics of the COVID-19 epidemic and to examine how these changes are associated with government intervention periods. For this purpose, a normalized dynamic SIR model is considered in which the recovery rate, $ \gamma $, is set to $ 1/14 $ day-1 in the primary analysis, while the transmission rate, $ \beta $, is allowed to vary across the periods identified in the analysis rather than being assumed constant. Changes in the case series are identified using change-point analysis, and the resulting model is solved using the Taylor collocation method. The estimated transmission rates are compared across the full-closure, partial-closure, and gradual-normalization periods using non-parametric statistical methods. The Kruskal–Wallis test revealed a statistically significant overall difference in the estimated transmission rates among the three intervention groups ($ H(2) = 14.353 $, $ p = 0.001 $). Subsequent pairwise comparisons using Dunn's post-hoc test with Bonferroni correction indicated significant differences between the full-closure and partial-closure periods and between the full-closure and gradual-normalization periods, whereas the difference between the partial-closure and gradual-normalization periods was not statistically significant. Sensitivity analyses using alternative recovery-rate assumptions ($ \gamma = 1/10 $ and $ \gamma = 1/20 $) yielded the same inferential pattern. These findings indicate that the estimated transmission rates varied across the intervention periods and illustrate the potential of the proposed dynamic SIR framework for characterizing temporal transmission patterns under changing intervention conditions.
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Figures(6) / Tables(10)
Serpil Ünal, Elçin Çelik, Deniz Uçar. A dynamic SIR epidemic model with the Taylor collocation method: Analysis of transmission dynamics under intervention changes[J]. AIMS Mathematics, 2026, 11(11): 36379-36408. doi: 10.3934/math.20261408
Timeline of the government interventions considered in the study
CUSUM chart for the COVID-19 case series
Detected change points and their corresponding bootstrap confidence levels. The dashed horizontal line indicates the 80% bootstrap confidence threshold used as the criterion for retaining detected change points
Estimated transmission rates across intervention segments. Horizontal segments indicate the time interval over which each estimated transmission rate was assumed constant
Box plots of the estimated transmission rates across the intervention groups
Observed active cases and the hypothetical epidemic trajectory obtained under the representative full-closure transmission rate $ \beta = 0.0654 $ with $ \gamma = 1/14 $. The simulation starts on 27 March 2020 and covers a 50-day period
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