Fast estimation of time-varying infectious disease transmission rates

Author summary Many pathogens cause recurrent epidemics. Patterns of recurrence are strongly affected by seasonality of the transmission rate, which can arise from seasonal changes in weather and host population behaviour (e.g., aggregation of children in schools). To understand and predict recurrent epidemic patterns, it is essential to reconstruct the time-varying transmission rate, which is never observed directly. Existing transmission rate estimation methods tend to fall into one of two categories: accurate but too slow to apply to long time series of reported incidence, or fast but inaccurate unless the number of individuals initially susceptible to infection is known precisely. Here, we introduce and compare fast methods inspired by the algorithm that Fine and Clarkson pioneered in the early 1980s. The method that we suggest accurately reconstructs seasonally varying transmission rates, even with crude information about the initial size of the susceptible population. Compartmental epidemic models have been used extensively to study the historical spread of infectious diseases and to inform strategies for future control. A critical parameter of any such model is the transmission rate. Temporal variation in the transmission rate has a profound influence on disease spread. For this reason, estimation of time-varying transmission rates is an important step in identifying mechanisms that underlie patterns in observed disease incidence and mortality. Here, we present and test fast methods for reconstructing transmission rates from time series of reported incidence. Using simulated data, we quantify the sensitivity of these methods to parameters of the data-generating process and to mis-specification of input parameters by the user. We show that sensitivity to the user's estimate of the initial number of susceptible individuals-considered to be a major limitation of similar methods-can be eliminated by an efficient, "peak-to-peak" iterative technique, which we propose. The method of transmission rate estimation that we advocate is extremely fast, for even the longest infectious disease time series that exist. It can be used independently or as a fast way to obtain better starting conditions for computationally expensive methods, such as iterated filtering and generalized profiling.