Reconstruction of disease transmission rates: Applications to measles, dengue, and influenza

Transmission rates are key in understanding the spread of infectious diseases. Using the framework of compartmental models, we introduce a simple method to reconstruct time series of transmission rates directly from incidence or disease-related mortality data. The reconstruction employs differential equations, which model the time evolution of infective stages and strains. Being sensitive to initial values, the method produces asymptotically correct solutions. The computations are fast, with time complexity being quadratic. We apply the reconstruction to data of measles (England and Wales, 1948-1967), dengue (Thailand, 1982-1999), and influenza (U.S., 1910-1927). The Measles example offers comparison with earlier work. Here we re-investigate reporting corrections, include and exclude demographic information. The dengue example deals with the failure of vector-control measures in reducing dengue hemorrhagic fever (DHF) in Thailand. Two competing mechanisms have been held responsible: strain interaction and demographic transitions. Our reconstruction reveals that both explanations are possible, showing that the increase in DHF cases is consistent with decreasing transmission rates resulting from reduced vector counts. The flu example focuses on the 1918/1919 pandemic, examining the transmission rate evolution for an invading strain. Our analysis indicates that the pandemic strain could have circulated in the population for many months before the pandemic was initiated by an event of highly increased transmission.