Abstract
tsiR is an open source software package implemented in the R programming language designed to analyze infectious disease time-series data. The software extends a well-studied and widely-applied algorithm, the time-series Susceptible-Infected-Recovered (TSIR) model, to infer parameters from incidence data, such as contact seasonality, and to forward simulate the underlying mechanistic model. The tsiR package aggregates a number of different fitting features previously described in the literature in a user-friendly way, providing support for their broader adoption in infectious disease research. Also included in tsiR are a number of diagnostic tools to assess the fit of the TSIR model. This package should be useful for researchers analyzing incidence data for fully-immunizing infectious diseases.
Highlights
Mathematical models coupled with statistical inference techniques allow us to compare infectious disease theory and data, shedding light on transmission estimates, vaccine control strategies, and predicting future trends [1, 2]
Once the susceptible dynamics are reconstructed, the modeler is again faced with many more choices about the log-linear model, the generalized linear model (GLM) family and link, and which parameters to estimate and which to fix
We have developed the tsiR package to address this methodological challenge and facilitate a more straight-forward and widely-accessible model-fitting process
Summary
Mathematical models coupled with statistical inference techniques allow us to compare infectious disease theory and data, shedding light on transmission estimates, vaccine control strategies, and predicting future trends [1, 2]. In the TSIR framework, a regression model is first fitted between cumulative cases and cumulative births Assuming they are equal, the slope will be the reporting rate ρt and the residuals of the regression model, Zt provide the shape of the susceptible dynamics, St. using Eq 2 and setting the expectation to the mean, the log-linear equation shown in Eq 3 can be acquired. Once the susceptible dynamics are reconstructed, the modeler is again faced with many more choices about the log-linear model, the GLM family and link, and which parameters to estimate and which to fix (commonly, for the study of measles dynamics, α is fixed to be 0.97, and S" is occasionally fixed as well to be 0.035 based on analysis of pre-vaccination data from the United Kingdom [6, 12, 18]) This decision process can be implemented in a Bayesian framework, is a computationally more extensive task.
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