Elaydi S, Lozi R. Global dynamics of discrete mathematical models of tuberculosis.
J Biol Dyn 2024;
18:2323724. [PMID:
38493487 DOI:
10.1080/17513758.2024.2323724]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2023] [Accepted: 02/21/2024] [Indexed: 03/19/2024]
Abstract
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 R 0 which is based on the disease-free equilibrium, and a new net reproduction number R 0 ( E ∗ ) based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if R 0 ≤ 1 and unstable if R 0 > 1 . Moreover, the endemic equilibrium is locally asymptotically stable if R 0 ( E ∗ ) < 1 < R 0 .
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