Volume 19, Number 4, Winter 2011
PARAMETER ESTIMATION IN EPIDEMIC
Dedicated to Prof. H. I. Freedman on the occasion of his 70th birthday
MODELS: SIMPLIFIED FORMULAS
K. P. HADELER
Abstract. We consider the problem of identifying the time-dependent transmission rate from incidence data and from prevalence data in epidemic SIR, SIRS, and SEIRS models. We show closed representation formulas avoiding the computation of higher derivatives of the data or solving differential equations. We exhibit the connections between the formulas given in several recent papers. In particular we explain the difficulties to estimate the initial number of susceptible or, equivalently, the initial transmission rate.