The susceptible-transmissible-removed (STR) model is a deterministic compartment model, based on the susceptible-infected-removed (SIR) prototype. The STR replaces 2 SIR assumptions. SIR assumes that the emigration rate (due to death or recovery) is directly proportional to the infected compartment's size. The STR replaces this assumption with the biologically appropriate assumption that the emigration rate is the same as the immigration rate one infected period ago. This results in a unique delay differential equation epidemic model with the delay equal to the infected period. Hamer's mass action law for epidemiology is modified to resemble its chemistry precursor-the law of mass action. Constructing the model for an isolated population that exists on a surface bounded by the extent of the population's movements permits compartment density to replace compartment size. The STR reduces to a SIR model in a timescale that negates the delay-the transmissible timescale. This establishes that the SIR model applies to an isolated population in the disease's transmissible timescale. Cyclical social interactions will define a rhythmic timescale. It is demonstrated that the geometric mean maps transmissible timescale properties to their rhythmic timescale equivalents. This mapping defines the hybrid incidence (HI). The model validation demonstrates that the HI-STR can be constructed directly from the disease's transmission dynamics. The basic reproduction number ( R 0 ) is an epidemic impact property. The HI-STR model predicts that R 0 ∝ √ n where n is the population density, and is the ratio of time increments in the transmissible-and rhythmic timescales. The model is validated by experimentally verifying the relationship. R 0 's dependence on n is demonstrated for dropletspread SARS in Asian cities, aerosol-spread measles in Europe and non-airborne Ebola in Africa.

The recently derived Hybrid-Incidence Susceptible-Transmissible-Removed (HI-STR) prototype is a deterministic epidemic compartment model and an alternative to the Susceptible-Infected-Removed (SIR) model prototype. The HI-STR predicts that pathogen transmission depends on host population characteristics including population size, population density and some common host behavioural characteristics. The HI-STR prototype is applied to the ancestral Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2) to show that the original estimates of the Coronavirus Disease 2019 (COVID-19) basic reproduction number ($\mathcal{R}_0$) for the United Kingdom (UK) could have been projected on the individual states of the United States of America (USA) prior to being detected in the USA. The Imperial College London (ICL) R0 estimate for the UK is projected onto each USA state. The difference between these projections and ICL estimates for USA states is either not statistically significant on the paired student t-test or epidemiologically insignificant. Projection provides a baseline for evaluating the real-time impact of an intervention. Sensitivity analysis was conducted because of considerable variance in parameter estimates across studies. Although the HI-STR predicts that increasing symptomatic ratio and inherently immune ratio reduce R0, relative to the uncertainty in the estimates of R0 for the ancestral SARS-CoV2, the projection is insensitive to the inherently immune ratio and the symptomatic ratio.