The initial exponential growth rate of an epidemic is an important measure of the severeness of the epidemic, and is also closely related to the basic reproduction number. Estimating the growth rate from the epidemic curve can be a challenge, because of its decays with time. For fast epidemics, the estimation is subject to over-fitting due to the limited number of data points available, which also limits our choice of models for the epidemic curve. We discuss the estimation of the growth rate using maximum likelihood method and simple models.

There currently is a severe Zika Virus (ZIKV) epidemic in Brazil and other South American countries. Due to international travel, this poses severe public health risk of ZIKV importation to other countries. We estimate the prevalence of ZIKV in an import region by the time a microcephaly case is detected, since microcephaly is presently the most significant indication of ZIKV presence. We establish a mathematical model to describe ZIKV spread from a source region to an import region. This model incorporates both vector transmission (between humans and mosquitoes) and sexual transmission (from males to females). We take account of population structure through a contact network for sexually active individuals. Parameter values of our model are either taken from the literature or estimated from travel data. This model gives us the probability distribution of time until detection of the first microcephaly case. Based on current field observations, our results also indicate that the percentage of infected pregnant women that results in fetal abnormalities is more likely to be on the smaller end of the 1%–30% spectrum that is currently hypothesized. Our model predicts that for import regions with at least 250,000 people, on average 1,000–12,000 will have been infected by the time of the first detection of microcephaly, and on average 200–1,500 will be infectious at this time. Larger population sizes do not significantly change our predictions. By the first detection of a microcephaly case, a sizable fraction of the population will have been infected by ZIKV. It is thus clear that adequate surveillance, isolation, and quarantine are needed in susceptible import regions to stop the dissemination of a Zika epidemic.