Analysis of a stochastic mathematical model for tuberculosis with case detection

In this work, we investigate some qualitative properties of a stochastic dynamical model for tuberculosis with case detection. Using appropriately formulated stochastic Lyapunov functions, we derive sufficient conditions for the existence (and uniqueness) of an ergodic stationary distribution of the...

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Bibliographic Details
Published inInternational journal of dynamics and control Vol. 10; no. 3; pp. 734 - 747
Main Author Okuonghae, D.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2022
Springer Nature B.V
Subjects
Complexity
Control
Control and Systems Theory
Dynamic models
Dynamical Systems
Engineering
Liapunov functions
Tuberculosis
Vibration
Ergodic stationary distribution
Tuberculosis
92B05
93E15
93E03
Stochastic Lyapunov function
Disease eradication
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Summary:In this work, we investigate some qualitative properties of a stochastic dynamical model for tuberculosis with case detection. Using appropriately formulated stochastic Lyapunov functions, we derive sufficient conditions for the existence (and uniqueness) of an ergodic stationary distribution of the positive solutions of the model, guaranteeing persistence of the disease in the presence of case detection. We also obtained conditions that will allow for the eradication of the disease from the population. Using numerical simulations, we were able to illustrate the analytical results obtained herein.
ISSN:2195-268X
2195-2698
DOI:10.1007/s40435-021-00863-8