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. 2025 Jul 30;15(1):27737.
doi: 10.1038/s41598-025-13287-7.

Optimal intervention design for tonsillitis transmission via compartmental modeling with stability analysis and control strategies

Mehmet Gümüş  1 , Shewafera Wondimagegnhu Teklu  2 , Aleyna Sezgin  2
Affiliations

Optimal intervention design for tonsillitis transmission via compartmental modeling with stability analysis and control strategies

Mehmet Gümüş et al. Sci Rep. .

Abstract

Tonsillitis represents a significant public health concern, particularly for children and adolescents, leading to substantial socioeconomic costs. To address this, we developed a compartmental mathematical model to investigate the disease's transmission dynamics and determine optimal intervention strategies. The model's analysis establishes the conditions for disease persistence and eradication. Using optimal control theory, we assessed the effectiveness of preventative measures as well as treatments for both acute and chronic stages of the infection. Our findings demonstrate that a multi-faceted approach is superior to any single strategy. The most effective and robust reduction in disease prevalence is achieved by an integrated strategy that combines prevention with enhanced treatment protocols. This study offers a quantitative tool for public health officials, providing an evidence-based framework to design and implement more effective policies for controlling tonsillitis.

Keywords: Compartmental model; Infection; Stability analysis, optimal control theory; Tonsillitis.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Population flow diagram of the tonsillitis infection spreading dynamics where formula image is described in the Eq. (2).
Fig. 2
Fig. 2
Forward bifurcation curve of the model.
Fig. 3
Fig. 3
Simulation graph for sensitivity indices.
Fig. 4
Fig. 4
Effect of formula image on formula image.
Fig. 5
Fig. 5
Effect of formula imageon formula image.
Fig. 6
Fig. 6
Effect of formula imageon formula image.
Fig. 7
Fig. 7
The tonisilitis model (3) solutions behavior in the case of formula image.
Fig. 8
Fig. 8
The tonisilitis model (3) solutions behavior in the case of formula image.
Fig. 9
Fig. 9
Impact of transmission rate on the total infected population.
Fig. 10
Fig. 10
Impact of treatment rate on the total infected population.
Fig. 11
Fig. 11
Impacts of control measure formula image the total tonsillitis infected population (A + C).
Fig. 12
Fig. 12
Impacts of control measure formula image the total tonsillitis infected population (A + C).
Fig. 13
Fig. 13
Impacts of control measure formula image the total tonsillitis infected population (A + C).
Fig. 14
Fig. 14
Impacts of control measure ( formula image the total tonsillitis infected population (A+C).
Fig. 15
Fig. 15
Impacts of control measure ( formula image the total tonsillitis infected population (A+C).
Fig. 16
Fig. 16
Impacts of control measure ( formula image the total tonsillitis infected population (A+C).
Fig. 17
Fig. 17
Impacts of Scenario 3 (formula image) control strategy on the total tonsillitis infected population (A+C).
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