Abstract

THE INTERACTIVE STAGES OF DISEASE TRANSITIONAND THEIRNEUTROSOPHICPROJECTION MATRIX WITH

A. Zubairu, A.A Ibrahim, A. Mustafa

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Abstract The classical SIR disease model was extended to include the exposed stage where the host population is composed of susceptible (S), Exposed (E) Infected (I ?) and recovered individuals (R). Such that the total population size at any given time N(t) will be N(t)=S(t)+E(t)+I ?(t)+R(t)and the generating function is given by A_n= (P_n-1)/2 P_n=1,3,5,7. So we attached an indeterminate factor "I" to A_n and obtained N(G)=A_n?I a neutrosophic group. Here also we show the interaction between two successive stages and their corresponding effects on the cyclic nature of disease transition. Finally the results were portrayed on the neutrosophic projection matrix so that important epidemiological quantities such as (R_0 ) and (?) could easily be estimated. Keywords: Generating function, Neutrosophic algebra, cyclic transition, projection matrix.

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