Fluctuations, control and suppression of viral outbreaks

Viral epidemics are always spread through population contacts that fluctuate, sometimes deterministically but mostly as random processes. Such fluctuations are observed in different spatial resolutions as well as time. Moreover, they affect how successful controls will be, whether through vaccinations, anti-virals, or social distancing-- as seen in the data analysis of COVID-19. Here we review how various controls will operate under different situations, with and without vaccination.

In the absence of vaccines and treatments, as in onset of the COVID-19 pandemic, societies must rely on non-pharmaceutical intervention strategies to control the spread of emerging diseases. We develop an analytical theory for COVID-19-like diseases propagating through networks using an SEIR-like model, showing how characteristic closure periods emerge that minimize the total disease outbreak, and increase predictably with the reproductive number and incubation periods of a disease as long as both are within predictable limits. Using our approach we demonstrate a sweet-spot
effect in which optimal periodic closure is maximally effective for diseases with similar
incubation and recovery periods.

Using a model reduction approach, we show that given measurements of incidence of cases, we can estimate the fraction of asymptomatics in diseased populations from time-series data. Since asymptomatics are typically a major fraction of the population driving the force of infection, we include them in an adaptive network population model with vaccination and temporary link de-activation. We show that vaccine control is much more effective in adaptive networks than in static networks due to feedback interaction between the adaptive network rewiring with temporary link deactivation and the vaccine application. When compared to extinction rates in static social networks, we expect that the amount of vaccine resources required to sustain similar rates of extinction is much lower in adaptive networks.