An epidemiological forecast model and software assessing interventions on COVID-19 epidemic in China

Peter X Song; Lili Wang; Yiwang Zhou; Jie He; Bin Zhu; Fei Wang; Lu Tang; Marisa Eisenberg

φptq " Here we show several examples of multi-point instantaneous quarantine rates in Figure 6 with jump sizes equal to φ 0 " pφ 01 , φ 02 , φ 03 q that occur respectively at dates of (Jan 23, Feb 4, Feb 8). In particular, we plot three scenarios, e.g., no intervention (φ 0 " p0, 0, 0q), multiple moderate jumps (φ 0 " p0.1, 0.4, 0.3q), and only one large jump (φ 0 " p0, 0.9, 0q). Note that at each jump, the respective proportion of the susceptible population would move to the quarantine compartment. For example, with φ 0 " p0.1, 0.4, 0.3q, the quarantine compartment will be enlarged accumulatively over three time points as 0.1 θ S t 1`0 .4θ S t 2`0 .3θ S t 3 . The f pθ t´1 , β, γq function determined by the above extended SIR model (6) can be solved by applying the fourth-order Runge-Kutta approximation, and the resulting solution is given in Figure 6 : Three examples of multi-point instantaneous quarantine rates. Subfigures from A to C denote φ 0 " p0, 0, 0, 0q, φ 0 " p0.1, 0.4, 0.3q and φ 0 " p0, 0.9, 0q at three time points of (Jan 23, Feb 4, Feb 8) respectively. Appendix A. To deal with the Dirac delta function φptq, we develop a two-step approximation for model (6) . In brief, we first solve a continuous function without change points via the differential equations in (5) , and then we directly move φptqθ S t of the susceptible compartment to the quarantine compartment. From our experience, this approach largely improves the approximation accuracy in the presence of discontinuities.