  Cure rate models are mostly used to study data arising from cancer clinical
trials. Its use in the context of infectious diseases has not been explored
well. In 2008, Tournoud and Ecochard first proposed a mechanistic formulation
of cure rate model in the context of infectious diseases with multiple
exposures to infection. However, they assumed a simple Poisson distribution to
capture the unobserved pathogens at each exposure time. In this paper, we
propose a new cure rate model to study infectious diseases with discrete
multiple exposures to infection. Our formulation captures both over-dispersion
and under-dispersion with respect to the count on pathogens at each time of
exposure. We also propose a new estimation method based on the expectation
maximization algorithm to calculate the maximum likelihood estimates of the
model parameters. We carry out a detailed Monte Carlo simulation study to
demonstrate the performance of the proposed model and estimation algorithm. The
flexibility of our proposed model also allows us to carry out a model
discrimination. For this purpose, we use both likelihood ratio test and
information-based criteria. Finally, we illustrate our proposed model using a
recently collected data on COVID-19.
