Fig. 1

Mathematical models are a useful tool for exploring the potential effects of NPIs against COVID-19. a Reducing transmission leads to a “flattening” of the epidemic curve, whereby the peak number of simultaneously infected individuals is smaller and the peak occurs later. b, c Simple models such as the SIR model can be extended to include features such as asymptomatic infectious individuals (b) and different contact rates between individuals of different ages (c). d When intense interventions are removed, case numbers may begin to increase again. In a, the numerical solution of the SIR model (system of Eq.s (1)) is shown for high transmissibility (R₀ = 3, blue line) and low transmissibility (R₀ = 2, red line), starting with S = 99,999, I = 1 and R = 0. In c, data show the average numbers of daily contacts that an individual in the age group on the x-axis has with contacts in the age group on the y-axis, in the UK under normal circumstances [4]. Ages are binned into 5-year intervals (with individuals and contacts who are over 80 years old included in the 75–80 age group). In d, the numerical solution of the SIR model (system of Eq.s (1)) is shown with R₀ = 0.9 for all times t ≤ 75 days, and R₀ = 1.5 for all times t > 75 days, starting with S = 99,000, I = 1000 and R = 0. In a and d, the infectious period is set to be 1/μ = 5 days