Abstract

Cyclic disease transition state and its correspondingneutrosophicprojection matrix with generating functionA_n= (P_n-1)/2 P_n=1,2,3.

1A.Zubairu, 2A.A Ibrahim, 3A. Mustapha

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Abstract Aunu permutation patterns A_n= (P_n-1)/2 P_n?5 are a class of (123) and (132) avoiding permutations patterns of prime cardinality and is being applied extensively in groups, graphs, cellular algebra, circuit design Automata theory, lattices, and association schemes among others [1]. This paper considered a different class of permutation pattern with generating function A_n= (P_n-1)/2 P_n=1,2,3and its application to cyclic disease transmission. We restricted ourselves to the classical S,I,R model but within the framework provided, cyclic disease transition graphs and their corresponding neutrosophic projection matrix can be derived for any disease with discrete disease states from which, important statistics such as population growth rate (?) and basic reproduction ratio (R_o ) could be estimated. Keywords Generating function, Neutrosophic algebraic structure, cyclic transition, projection matrix.

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