New coronavirus outbreak. Lessons learned from the severe acute respiratory syndrome epidemic

Abstract

System dynamics approach offers great potential for addressing how intervention policies can affect the spread of emerging infectious diseases in complex and highly networked systems. Here, we develop a model that explains the severe acute respiratory syndrome coronavirus (SARS-CoV) epidemic that occurred in Hong Kong in 2003. The dynamic model developed with system dynamics methodology included 23 variables (five states, four flows, eight auxiliary variables, six parameters), five differential equations and 12 algebraic equations. The parameters were optimized following an iterative process of simulation to fit the real data from the epidemics. Univariate and multivariate sensitivity analyses were performed to determine the reliability of the model. In addition, we discuss how further testing using this model can inform community interventions to reduce the risk in current and future outbreaks, such as the recently Middle East respiratory syndrome coronavirus (MERS-CoV) epidemic.

Keywords: Emerging infections; MERS-CoV; SARS-CoV; epidemics; modelling.

Fig. 1.

Real data from the Hong Kong SARS outbreak. (a) Daily reported new cases, deaths, and recovered. (b) Cumulative cases, dead, and recovered.

Fig. 2.

Graphical description of the model using Vensim software. Stock variables are represented inside boxes; flow variables are designed as arrows with a valve; the rest of the variables are auxiliary (inside circles) or parameters (in bold); single lines with arrow are used as connectors to specify that the destination variable is affected by the variable of origin.

Fig. 3.

Normalized representation of repression Hill function. The solid line corresponds to a value of n = 3 [as used in equation (7) of Table 3]. The dotted line corresponds to the threshold repression function (when n tends to infinity). The representation is normalized to the threshold of cumulative attack rate on the abscissa axis and the value of the discontinuity (daily contacts) on the ordinate axis.

Fig. 4.

Simulation of the model. For simulation, the time period was set to 146 days with a time step of 1 day. The graphs represent the output of the simulation (solid lines) and the data reported for the SARS outbreak (dotted lines). (a) Sick per day, (b) cumulative cases, (c) recovered, (d) dead, (e) daily recovered, and (f) daily deaths.

Fig. 5.

Basic reproductive number obtained from the simulation. R₀ was calculated as the ratio between the contagion rate and the recovery rate.

Fig. 6.

Sensitivity of the model to changes in parameters. Univariate analysis with 1000 simulations was performed for each parameter: (a) case fatality, (b) threshold of cumulative attack rate, (c) disease duration, (d) infectivity, (e) daily contacts, and (f) incubation period. The parameters were varied considering ranges and distributions shown in Table 5. The solid black line represents the simulation output and the grey area represents the 95% confidence bounds.

Fig. 7.

Multivariate sensitivity analysis of the model. A Monte-Carlo sensitivity analysis with 1000 simulations was performed and the results for (a) sick per day, (b) infected, (c) recovered, and (d) dead are shown. The values of the six parameters were altered at the same time following the distributions described in Table 5. The solid black line represents the simulation output and the grey area represents the 95% confidence bounds.