A two-strain tuberculosis model with age of infection. (English) Zbl 1017.35066

A two-strain tuberculosis (TB) model with arbitrarily distributed delays in the latent class of individuals with drug-sensitive TB is considered. The adjectives active, infectious and infective are used as synonyms and latent means infected but not infectious. Based on the treatment failure rate \(q\) of the individuals infected with drug-sensitive TB, two scenarios are here considered: (a) The case \(q=0\) corresponding to the situation where all treated individuals finish their treatment and new cases of drug-resistant TB are produced only through contact with individuals with that; (b) The case \(q>0\) meaning a fraction of treated individuals with drug-sensitive TB will develop resistance due to incomplete treatment. The existence of steady states is established and the reproductive numbers associated with each strain are calculated. Using the reproductive numbers, the dynamics such as stability properties of the model are studied.


35L60 First-order nonlinear hyperbolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
92D25 Population dynamics (general)
92D30 Epidemiology
45D05 Volterra integral equations
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