Global dynamics of approximate solutions to an age-structured epidemic model with diffusion |
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Authors: | M Y Kim |
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Institution: | (1) Department of Mathematics, Inha University, Inchon, 402-751, South Korea |
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Abstract: | We consider an age-dependent s-i-s epidemic model with diffusion whose mortality is unbounded. We approximate the solution using Galerkin methods in the space
variable combined with backward Euler along the characteristic direction in the age and time variables. It is proven that
the scheme is stable and convergent in optimal rate in l
∞,2 (L
2) norm. To investigate the global behavior of the discrete solution resulting from the algorithm, we reformulate the resulting
system into a monotone form. Positivity of the nonlocal birth process is proved using the positivity of the first eigenvalue
of the resulting matrix system and using the fact that the positivity is preserved along the characteristics. The difference
equation of the steady state coupled with nonlocal birth process is solved by developing monotone iterative schemes. The stability
of the discrete solution of the steady state is then analyzed by constructing suitable positive subsolutions.
Mathematics subject classifications (2000) 65M12, 65M25, 65M60, 92D25
M.-Y. Kim: This work was supported by Korea Research Foundation Grant (KRF-2001-041-D00037). |
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Keywords: | s-i-s epidemic model integro-differential equation Galerkin method characteristic method error estimates asymptotic behavior |
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