Giordano2020 - Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy

September 2020, Model of the Month by Kausthubh Ramachandran

Original model - BIOMD0000000955

Background:

The Coronavirus Disease outbreak 2019 (COVID-19), caused by the novel betacoronavirus SARS-Cov-2,  emerged in early December 2019 in Wuhan, China and has since spread to over 227 countries (ArcGIS, JHU. 2020). The World Health Organisation declared COVID-19 to be a public health emergency of the highest order (Timeline of WHO’s response. 2020). Forecasting the pandemic using predictive mathematical models is necessary to help policymakers decide the type, chronology, and intensity of crisis management measures to maximally mitigate the negative impacts of the pandemic (Hethcote 2000). A common ODE-based model used is the Susceptible(S) - Infected(I) - Recovered(R) model or SIR model (Kermack, W O et al. 1927). In this model, the population is classified into three mutually exclusive categories S, I, and R and the movement of members of the population from S to R is described by rate laws. For the COVID-19 pandemic, several models have been proposed based on the SIR model with varying degrees of complexity to account for the asymptomatic spreaders (Rothe C et al. 2020), differing social mixing patterns (Prem et al. 2020), varying demographics and government responses. 

 

Figure 1 - graphical representation of the SIDARTHE model (Reproduced from Giordano 2020)

 

Giordano et al constructed a 8-compartment SIDARTHE model to analyse the transmission dynamics of COVID-19 in Italy (Giordano et al. 2020). To account for the significant spread of COVID-19 due to asymptomatic patients and undetected carriers, the infected population was divided into 5 compartments - Infected(I), Recognised(R), Ailing(A), Diagnosed(D), and Threatened(T) (Figure 1). This classification created restrictions on how different sections of the population contribute to COVID-19 spread, quantified the long-term effects of inadequate testing, and helped understand the possible impact of different lockdown measures. The ODEs for the model are shown in Figure 2.


 

Figure 2 - ODEs for the SIDARTHE model (reproduced from Giordano 2020).

S - Susceptible, I - Infected, D - Diagnosed, A - Ailing, R - Recovered, T - Threatened (patients in critical condition), H - Hospitalied, E - Extinct.

 

Results and discussion:

The model simulates and forecasts the possible progression of the pandemic from day 0 onwards in Italy under different lockdown scenarios and analyses their impact on the basic reproduction number (Ro) of the pandemic. In one scenario, the model explores the consequences of either weakening or strengthening social distancing measures after day 50 and finds that it takes a longer time for the infection curve to flatten out when social distancing is weakened (Figure 3). 

 

Figure 3 - Evolution of COVID-19 transmission when countermeasures like social distancing are weakened after day 50 (reproduced version of Figure 3b from the manuscript)

The authors advocate for widespread testing and diagnosis campaigns and have demonstrated that their implementation reduces the peak of the infection curve and controls the spread quicker. In the model, the authors simulated conditions of stringent testing and contact tracing measures enforced after day 50. They also account for weakening social distancing measures and find that the infection curves flattens quickly in the presence of high levels of testing and contact tracing despite weaker social distancing (Refer Fig 4b and 4d in the manuscript).

The model also makes a distinction between undetected and detected cases and helps to evaluate the long-term effects of inadequate testing. This helps quantify the observed discrepancy between actual case-fatality rate (total number of deaths due to the infection per the total number of infections) and the perceived case-fatality rate (number of deaths attributed to the infection per the total number of diagnosed cases). In the absence of adequate testing, the transmission rate will be underestimated and the case-fatality rate will be inflated. 

In conclusion, the authors created a comprehensive model to quantify the effects of policy decisions like social distancing and widespread testing on key pandemic parameters like basic reproduction number. The model provides policymakers with a tool to analyse the outcomes of different lockdown strategies.

 

References:

  1. "COVID-19 Dashboard by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU)". ArcGIS. Johns Hopkins University. Retrieved 28 August 2020.

  2. Timeline of WHO’s response to COVID-19. Last updated 30 July 2020

  3. Hethcote W H. The Mathematics of Infectious Diseases. 2000. SIAM Review. 42:4 599-653 

  4. Kermack, W O et al. A contribution to the mathematical theory of epidemics. 1927. Proc. R. Soc. Lond. 115, 700–721

  5. Rothe C et al. Transmission of 2019-nCoV infection from an asymptomatic contact in Germany. 2020. N Engl J Med; published online Jan 30. DOI:10.1056/NEJMc2001468.

  6. Prem et al. The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study. 2020. Lancet Public Health. DOI:10.1016/S2468-2667(20)30073-6

  7. Giordano G et al. Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. 2020. Nature Medicine. 26, 855-860