Global Stability for an Endogenous-Reactivated Tuberculosis Model with Beddington-DeAngelis Incidence, Distributed
Yuan Sang1,2, Long Zhang1,2, Bing Song1,2
1College of Mathematics and Systems Science, Xinjiang University, Ürümqi, 830017 People's Republic of China.
Qualitative Theory of Dynamical Systems
|May 1, 2023
Summary
This study models tuberculosis (TB) spread, finding distributed delays increase TB persistence. Enhancing protection for susceptible and infectious individuals is key to controlling this disease.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- Tuberculosis (TB) remains a significant global health challenge.
- Understanding TB transmission dynamics is crucial for effective control strategies.
Purpose of the Study:
- To develop and analyze a mathematical model for TB epidemics incorporating Beddington-DeAngelis incidence and distributed delays.
- To investigate the impact of latent periods, reactivation, treatment, and relapse on TB dynamics.
Main Methods:
- Formulation of a novel TB epidemic model with distributed delay.
- Analysis of the basic reproduction number (R0) to determine disease-free and endemic equilibria.
- Validation of theoretical findings using numerical simulations.
Main Results:
- The model's stability analysis revealed conditions for disease-free and endemic equilibria based on R0.
- Numerical simulations indicated that distributed delays can lead to increased TB persistence compared to discrete delays.
- Model simulations showed that enhancing protection levels for susceptible and infectious individuals is vital for TB control.
Conclusions:
- The proposed TB model provides insights into disease persistence influenced by distributed delays.
- Interventions focusing on increasing population protection are essential for managing TB epidemics.
Keywords:
Beddington–DeAngelis incidenceDistributed delayEndogenous reactivationGlobal stabilityTuberculosisMore Related Videos
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