Estimating Time-Dependent Disease Transmission Intensity using Reported Data: An Application to Ebola and Selected Public Health Problems

Abstract

Obtaining reasonable estimates for transmission rates from observed data is a challenge when using mathematical models to study the dynamics of infectious diseases, like Ebola. Most models assume the transmission rate of a contagion does not vary over time. However, these rates do vary during an epidemic due to environmental conditions, social behaviors, and public-health interventions deployed to control the disease. Therefore, obtaining time-dependent rates can aid in understanding the progression of disease through a population. We derive an analytical expression using a standard SIR-type mathematical model to compute time-dependent transmission rate estimates for an epidemic in terms of either incidence or prevalence type available data. We illustrate applicability of our method by applying data on various public health problems, including infectious diseases (Ebola, SARS, and Leishmaniasis) and social issues (obesity and alcohol drinking) to compute transmission rates over time. We show that transmission rate estimates can have a large variation over time, depending on the type of available data and other epidemiological parameters. Time-dependent estimation of transmission rates captures the dynamics of the problem and can be utilized to understand disease progression through population accurately. Alternatively, constant estimations may provide unacceptable results that could have major public health consequences.