Page 211 - IJOCTA-15-4

Data-driven optimization and parameter estimation for an epidemic model
Table 1. Vertex numbers and corresponding cities of the Poland road network

Vertex - City/ies Vertex - City/ies
1 - Pozna´n 12 - Bia lystok
2 - Wroc law 13 - Szczecin
3 - Katowice, Sosnowiec, Zabrze, & Bytom 14 - Kielce
4 - Krak´ow 15 - Czestochowa
5 - Rzesz´ow 16 - Bydgoszcz
6 - Radom 17 - Suwa lki
7 - L´od´z 18 - Zielona G´ora
8 - Warszawa (Warsaw) 19 - Gorz´ow Wielkopolski
9 - Gda´nsk & Gdynia 20 - Rybnik
´
10 - Bielsko-Bia la 21 - Swinouj´scie
11 - Lublin 22 - Toru´n

Figure 1. Simplified road network of Poland with E-road classification by edge.

P 2
are 3|V | + |E| + deg(v) parameters, which
v
are first estimated using data and then adjusted d
using optimization, as discussed in Section 2.3. dt I v = β v S v I v − η v I v
 
(2)
X X v
Here, we state the model under consideration, + α v I e (v, t) −  λ e  I v
offering explanations of the equations in the sub- e|e∼v e|e∼v
sequent paragraphs:

Vertices Edges
d ∂ ∂ 2
S v = −β v S v I v (1) I e = d e I e (3)
dt ∂t ∂x 2
753