Machine learning for mathematical models of HCV kinetics during antiviral therapy.

Mathematical models for hepatitis C virus (HCV) dynamics have provided a means for evaluating the antiviral effectiveness of therapy and estimating treatment outcomes such as the time to cure. Recently, a mathematical modeling approach was used in the first proof-of-concept clinical trial assessing in real-time the utility of response-guided therapy with direct-acting antivirals (DAAs) in chronic HCV-infected patients. Several retrospective studies have shown that mathematical modeling of viral kinetics predicts time to cure of less than 12 weeks in the majority of individuals treated with sofosbuvir-based as well as other DAA regimens. A database of these studies was built, and machine learning methods were evaluated for their ability to estimate the time to cure for each patient to facilitate real-time modeling studies. Data from these studies exploring mathematical modeling of HCV kinetics under DAAs in 266 chronic HCV-infected patients were gathered. Different learning methods were applied and trained on part of the dataset ('train' set), to predict time to cure on the untrained part ('test' set). Our results show that this machine learning approach provides a means for establishing an accurate time to cure prediction that will support the implementation of individualized treatment.

Determinants of periodicity in seasonally driven epidemics.

Seasonality strongly affects the transmission and spatio-temporal dynamics of many infectious diseases, and is often an important cause for their recurrence. However, there are many open questions regarding the intricate relationship between seasonality and the complex dynamics of infectious diseases it gives rise to. For example, in the analysis of long-term time-series of childhood diseases, it is not clear why there are transitions from regimes with regular annual dynamics, to regimes in which epidemics occur every two or more years, and vice-versa. The classical seasonally-forced SIR epidemic model gives insights into these phenomena but due to its intrinsic nonlinearity and complex dynamics, the model is rarely amenable to detailed mathematical analysis. Making sensible approximations we analytically study the threshold (bifurcation) point of the forced SIR model where there is a switch from annual to biennial epidemics. We derive, for the first time, a simple equation that predicts the relationship between key epidemiological parameters near the bifurcation point. The relationship makes clear that, for realistic values of the parameters, the transition from biennial to annual dynamics will occur if either the birth-rate (µ) or basic reproductive ratio (R(0)) is increased sufficiently, or if the strength of seasonality (δ) is reduced sufficiently. These effects are confirmed in simulations studies and are also in accord with empirical observations. For example, the relationship may explain the correspondence between documented transitions in measles epidemics dynamics and concomitant changes in demographic and environmental factors.