Global dynamics of discrete mathematical models of tuberculosis

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional $ \mathcal {R}_0 $ R 0 which is...

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Bibliographic Details
Published in:Journal of biological dynamics 2024-12, Vol.18 (1), p.2323724-2323724
Main Authors: Elaydi, Saber, Lozi, René
Format: Article
Language:English
Subjects:
92-10
disease control
disease-free
endemic
endogenous
epidemiology
exogenous
global stability
Life Sciences
local stability
Mathematics
public health
SEI models
SEIT models
TB elimination
treatment
Tuberculosis
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Summary:In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional $ \mathcal {R}_0 $ R 0 which is based on the disease-free equilibrium, and a new net reproduction number $ \mathcal {R}_0(\mathcal {E}^*) $ R 0 ( E ∗ ) based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if $ \mathcal {R}_0 \leq ~1 $ R 0 ≤   1 and unstable if $ \mathcal {R}_0 \gt 1 $ R 0 > 1 . Moreover, the endemic equilibrium is locally asymptotically stable if $ \mathcal {R}_0(\mathcal {E}^*) \lt 1 \lt \mathcal {R}_0 $ R 0 ( E ∗ ) < 1 < R 0 .
ISSN:1751-3758
1751-3766
DOI:10.1080/17513758.2024.2323724