Vaccine clinical trials traditionally use the time to consequential human infection as the primary endpoint. A common method of analysis for such trials is to compare the times to infection between the vaccine and placebo groups using a Cox regression model. With new technology, we can additionally record the precise number of virions that cause infection rather than just the indicator that infection occurred. In this paper we develop a unified approach for vaccine trials that couples the time to infection with the number of infecting or founder viruses. We assume that the instantaneous risk of a potentially infectious exposure for individuals in the placebo and vaccine groups follows the same proportional intensity model. Following exposure, the number of founder viruses X* is assumed to be generated from some distribution on 0,1,..., which is allowed to be different for the two groups. Exposures that result in X*=0 are unobservable. We denote the placebo and vaccine means of X* by m and m D so that 1- D measures the proportion reduction in the mean number of infecting virions due to vaccination per exposure. We develop different semi-parametric methods of estimating D. We allow the distribution of X* to be Poisson or unspecified, and discuss how to incorporate covariates that impact the time to exposure and/or X*. Interestingly D, which is a ratio of untruncated means, can be reliably estimated using truncated data, even if the placebo & vaccine distributions of X* are completely unspecified. Simulations of vaccine clinical trials show that the method can reliably recover D in realistic settings. We apply our methods to an HIV vaccine trial conducted in injecting drug users.