Abstract. Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R0, the contact number σ, and the replacement number R are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for R0 are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of R0 and σ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.
The Molecular Evolutionary Genetics Analysis (MEGA) software has matured to contain a large collection of methods and tools of computational molecular evolution. Here, we describe new additions that make MEGA a more comprehensive tool for building timetrees of species, pathogens, and gene families using rapid relaxed-clock methods. Methods for estimating divergence times and confidence intervals are implemented to use probability densities for calibration constraints for node-dating and sequence sampling dates for tip-dating analyses. They are supported by new options for tagging sequences with spatiotemporal sampling information, an expanded interactive Node Calibrations Editor, and an extended Tree Explorer to display timetrees. Also added is a Bayesian method for estimating neutral evolutionary probabilities of alleles in a species using multispecies sequence alignments and a machine learning method to test for the autocorrelation of evolutionary rates in phylogenies. The computer memory requirements for the maximum likelihood analysis are reduced significantly through reprogramming, and the graphical user interface has been made more responsive and interactive for very big data sets. These enhancements will improve the user experience, quality of results, and the pace of biological discovery. Natively compiled graphical user interface and command-line versions of MEGA11 are available for Microsoft Windows, Linux, and macOS from www.megasoftware.net.
