Modeling the second wave of COVID-19 infections in France and Italy via a stochastic SEIR model

Late in the spring of this year, many nations around the world, especially in Europe, faced public health crises, as coronavirus infections threatened to overwhelm their intensive care facilities. Authorities responded with drastic measures to reduce social contacts, closing businesses and schools, restricting public transport and banning large social events. These “lockdown” measures were highly effective, greatly reducing infection numbers, yet were also expensive, entailing enormous economic, social and psychological costs. The International Monetary Fund estimates a 3% drop in global GDP for 2020. The measures created tens of millions of newly unemployed, as well as a surge in psychological issue including insomnia or anxiety.
Since then, nations have come out of the strictest forms of lockdown, and instead moved to contain the pandemic with more targeted measures based on detailed monitoring of the number of infected patients and deaths over time. In a recent paper, LML External Fellow Davide Faranda and colleagues have explored the prospects for such data-intensive monitoring to be successful, given the prevailing uncertainties in key aspects of the epidemic’s dynamics, and the inherent errors in infection counts. They use a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) model, which allows them to how epidemic progress might dependence on the enforcement or relaxation of confinement measures, or the influence of super-spreaders. Their modelling shows that the long-term outcomes are sensitive to both the initial conditions and the value of control parameters, with asymptotic estimates varying by as much as ten million.
The team also modelled future epidemic scenarios using various fluctuating trajectories for the basic reproductive number R0 and performing 30 realisations of the stochastic SEIR model. They found that, despite large uncertainties, distinct scenarios clearly appeared from the noise. In particular, the simulations suggest that a second wave could be avoided even with R0 values slightly larger than one. This implies that a second peak of infections could be avoided without the need for strict lockdown measures, if people followed other practices including reducing mobility and using surgical masks, and if authorities instituted effective contact tracking. In all cases, however, the presence of super-spreader events would make a second wave more likely. The latter scenario has been, unfortunately, verified by the current evolution of the epidemics in Italy and France. In both countries R0 values were above the critical threshold of one entraining a second wave and new lockdown measures. This result demonstrates that this simple model is capable of providing realistic epidemiological projections for countries with centralised management of the epidemic, France and Italy being two examples.
The paper is available at

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