An Analytic Approximate Solution of the SIR Model

The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced approximate ones, whose solutions given explicitly in terms functions, originating, piece-wisely, from generalized logistic functions: they ensure exact (in numerical sense) asymptotic values, besides to be quite practical use, for example with fit data algorithms; moreover unveil useful feature, that fact, at least very strict approximation, also owned (numerical) equations. novelties work are: way obtained, using simple, analytic geometry considerations; easy and formulation final solutions; mentioned never disclosed before. work’s method result prove robust over range values well known non-dimensional parameter called basic reproduction ratio, covers all epidemic cases, influenza measles: this point which doesn’t appear much discussed analogous works.