ABSTRACT
Martingales are certain random processes evolving in time. This chapter discusses the rich theory of martingales to set up estimating equations for important parameters and associated standard errors. The approach based on martingales then enables to estimate the infection rate, nonparametrically, as a function of time. Consider the problem of making inference about the infection rate of the simple epidemic model. The standard general epidemic model assumes that individuals become infectious immediately upon being infected. An individual’s infectious periods ends by his removal from circulation, which occurs by isolation, death or, more frequently, by the individual losing his infectiousness naturally and becoming immune from further infection. The present formulation assumes that each infective mixes uniformly with members of his own household and also mixes uniformly with individuals from other households. A household is taken to be a group of individuals residing in the same cottage.
