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Qualitative behavior of numerical solutions to an \(S-I-S\) epidemic model. (English) Zbl 0923.92023
Much work has been done on the numerical analysis of age-structured epidemic models. The author considers a nonlinear age-dependent S-I-S epidemic model converging uniformly to a steady state. He approximates the solution using finite differences along the characteristics and the backward Euler scheme which preserves the monotonicity properties of the original model. An explicit threshold condition for the existence of nontrivial steady states is provided. The linear case was studied by M. Iannelli et al. [SIAM. J. Math. Anal. 23, No.3, 662-688 (1992; Zbl 0776.35032)].

MSC:
92D30 Epidemiology
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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