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A Fibonacci model of infectious disease. (English) Zbl 0855.92021
Summary: The Fibonacci rabbit population model is often regarded as one of the first studies of population growth using mathematics. Later, an analytic model of population dynamics was introduced by Volterra. Systematic epidemic modeling in age-structured populations was first carried out in this century by F. Hoppensteadt [J. Franklin Inst. 297, 325-333 (1974; Zbl 0305.92010)].
F. Dubeau [Fibonacci Quart. 31, No. 3, 268-274 (1993; Zbl 0779.11008)], in revisiting the Fibonacci rabbit growth model, has developed an approach that can be applied to population dynamics and epidemiology where censoring occurs either by inability to procreate or by death. It is the purpose of this note to apply Dubeau’s method to a Fibonacci model of infectious diseases which was developed by A. Makhmudov [Mathematical modeling in immunology and medicine, Proc. IFIP TC7 Working Conf., Moscow 1982; 319-323 (1983; Zbl 0507.92018)], and to combine it with the approach of A. G. Shannon et al. [Comput. Math. Appl. 14, No. 9-12, 829-833 (1987)] who attempted to refine the work of Makhmudov.
92D30 Epidemiology
11B37 Recurrences
11B39 Fibonacci and Lucas numbers and polynomials and generalizations