Abstract
The novel coronavirus (SARS-CoV-2), identified in China at the end of December 2019 and causing the disease COVID-19, has meanwhile led to outbreaks all over the globe with about 2.2 million confirmed cases and more than 150,000 deaths as of April 17, 2020. In this work, mathematical models are used to reproduce data of the early evolution of the COVID-19 outbreak in Germany, taking into account the effect of actual and hypothetical non-pharmaceutical interventions. Systems of differential equations of SEIR type are extended to account for undetected infections, stages of infection, and age groups. The models are calibrated on data until April 5. Data from April 6 to 14 are used for model validation. We simulate different possible strategies for the mitigation of the current outbreak, slowing down the spread of the virus and thus reducing the peak in daily diagnosed cases, the demand for hospitalization or intensive care units admissions, and eventually the number of fatalities. Our results suggest that a partial (and gradual) lifting of introduced control measures could soon be possible if accompanied by further increased testing activity, strict isolation of detected cases, and reduced contact to risk groups.
Highlights
In late December 2019, several cases of acute respiratory syndrome were first reported in Wuhan City (Hubei region, China) by Chinese public health authorities
In this work we proposed a mathematical model for predicting the evolution in time of detected COVID-19 infections in Germany taking into account the age distribution of cases
Distinguishing between people in different age groups allows the model to better characterize contacts between individuals and to fine-tune the effect of intervention measures on contacts reduction
Summary
In late December 2019, several cases of acute respiratory syndrome were first reported in Wuhan City (Hubei region, China) by Chinese public health authorities. Early-stage detection has a similar small impact (S1(η0) = 0.05±0.03), while the probability of detection while symptomatic has an even lower impact (S1(η1) = 0.002 ±0.005), confirming the non-identifiability of this parameter Both the transmission rate of asymptomatic individuals and the probability of developing symptoms seem to have strong effects on the maximum number of active reported infections (S1(βU) = 0.32±0.05, S1(ρ0) = 0.42±0.06). This is a classical extension of the standard disease transmission model to account for non-exponential distributions of incubation and infectious periods (cf., e.g., [18] for another example of application in modeling COVID-19) This results in a total of one plus nine infective compartments per age class (stage E3 is assumed to be infective as well, as individuals have been reported to be infectious before symptoms onset [6, 11]). For each age class A we have the following compartments
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