Recently Gani  has considered a stochastic model for the attachment of phages to bacteria. In this paper we describe a simple method of estimating the parameter $\alpha$ which occurs in this model and study the asymptotic properties of the estimate.
"Estimation of The Parameter in the Stochastic Model for Phage Attachment to Bacteria." Ann. Math. Statist. 39 (1) 183 - 192, February, 1968. https://doi.org/10.1214/aoms/1177698517