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Global stability and periodic solution of a model for HTLV-I infection and ATL progression. (English) Zbl 1099.92042

Summary: Human \(T\)-cell lymphotropic virus I (HTLV-I) infection is linked to the development of adult \(T\)-cell leukemia/lymphoma (ATL), among many illness. The healthy \(CD4^{+}\) T cells infect HTLV-I through cell-to-cell contact with infected \(T\)-cells. The infected \(T\) cells can remain latent and harbor virus for several years before virus production occurs. Actively infected \(T\) cells can infect other \(T\) cells and can convert to ATL cells, whose growth is assumed to follow a classical logistic growth function. We consider a classical mathematical model with saturation response of the infection rate. By stability analysis we obtained the condition for the infected \(T\) cells die out and the condition for HTLV-I infection becomes chronic. At the same time, we also obtained the condition for a unique endemic equilibrium to be globally stable in the interior of the feasible region.

MSC:

92C50 Medical applications (general)
34D23 Global stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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