Rapid growth of the COVID-19 epidemic in China induced extensive efforts of contact tracing and social-distancing/lockdowns, which quickly contained the outbreak and has been replicated to varying degrees around the world. We construct a novel infectious disease model incorporating these distinct quarantine measures (contact tracing and self-quarantine) as reactionary interventions dependent on current infection levels. Derivation of the final outbreak size leads to a simple inverse proportionality relationship with self-quarantine rate, revealing a fundamental principle of exponentially increasing cumulative cases when delaying mass quarantine or lockdown measures beyond a critical time period. In contrast, contact tracing results in a proportional reduction in reproduction number, flattening the epidemic curve but only having sizable impact on final size when a large proportion of contacts are "perfectly" traced. We fit the mathematical model to data from China on reported cases and quarantined contacts, finding that lockdowns had an overwhelming influence on outbreak size and duration, whereas contact tracing played a role in reducing peak number of infected. Sensitivity analysis and simulations under different re-opening scenarios illustrate the differential effects that responsive contact tracing and lockdowns can have on current and second wave outbreaks.

Infectious disease dynamics operate across biological scales: pathogens replicate within hosts, but transmit among hosts and populations. Functional changes in the pathogen-host interaction thus generate cascading effects from molecular to landscape scales. We investigated within-host dynamics and among-host transmission of three strains of foot-and-mouth disease viruses (FMDVs) in their wildlife host, African buffalo. We combined data on viral dynamics and host immune responses with mathematical models to ask (i) How do viral and immune dynamics vary among FMDV strains? (SAT1, 2, 3); (ii) Which viral and immune parameters determine viral fitness within hosts?; and (iii) How do within-host dynamics relate to virus transmission among hosts? Our data reveal contrasting within-host dynamics among viral strains. However, SAT2 elicited more rapid and effective immune responses than SAT1 and SAT3. Within-host viral fitness was overwhelmingly determined by variation among hosts in immune response activation rates against FMDVs, but not by variation among individual hosts in viral growth rate. By contrast, our analyses investigating across-scale linkages indicate that viral replication rate in the host correlates with transmission rates among buffalo; and that adaptive immune activation rate determines the infectious period. Together, these parameters define the basic reproductive number of the virus, suggesting that viral invasion potential may be predictable from within-host dynamics. Future work should test the generality of these findings by including additional FMDV strains, and create a multi-scale model to link within-host and between-host dynamics explicitly.

The COVID-19 pandemic has led to widespread attention given to the notions of ”flattening the curve” during lockdowns, and successful contact tracing programs suppressing outbreaks. However a more nuanced picture of these interventions’ effects on epidemic trajectories is necessary. By mathematical modeling each as reactive quarantine measures, dependent on current infection rates, with different mechanisms of action, we analytically derive distinct nonlinear effects of these interventions on final and peak outbreak size. We simultaneously fit the model to provincial reported case and aggregated quarantined contact data from China. Lockdowns compressed the outbreak in China inversely proportional to population quarantine rates, revealing their critical dependence on timing. Contact tracing had significantly less impact on final outbreak size, but did lead to peak size reduction. Our analysis suggests that altering the cumulative cases in a rapidly spreading outbreak requires sustained interventions that decrease the reproduction number close to one, otherwise some type of swift lockdown measure may be needed.

Each state in the USA exhibited a unique response to the COVID-19 outbreak, along with variable levels of testing, leading to different actual case burdens in the country. In this study, via per capita testing dependent ascertainment rates, along with case and death data, we fit a minimal epidemic model for each state. We estimate infection-level responsive lockdown/self-quarantine entry and exit rates (representing government and behavioural reaction), along with the true number of cases as of 31 May 2020. Ultimately, we provide error-corrected estimates for commonly used metrics such as infection fatality ratio and overall case ascertainment for all 55 states and territories considered, along with the USA in aggregate, in order to correlate outbreak severity with first wave intervention attributes and suggest potential management strategies for future outbreaks. We observe a theoretically predicted inverse proportionality relation between outbreak size and lockdown rate, with scale dependent on the underlying reproduction number and simulations suggesting a critical population quarantine ‘half-life’ of 30 days independent of other model parameters.

Each state in the United States exhibited a unique response to the COVID-19 outbreak, along with variable levels of testing, leading to different actual case burdens in the country. In this study, via per-capita testing dependent ascertainment rates, along with case and death data, we fit a minimal epidemic model for each state. We estimate infection-level responsive lockdown entry and exit rates (representing government and behavioral reaction), along with the true number of cases as of May 31, 2020. Ultimately we provide error corrected estimates for commonly used metrics such as infection fatality ratio and overall case ascertainment for all 55 states and territories considered, along with the United States in aggregate, in order to correlate outbreak severity with first wave intervention attributes and suggest potential management strategies for future outbreaks. We observe a theoretically predicted inverse proportionality relation between outbreak size and lockdown rate, with scale dependent on the underlying reproduction number and simulations suggesting a critical population quarantine “half-life” of 30 days independent of other model parameters.