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. 2019 Mar 6;470:20–29. doi: 10.1016/j.jtbi.2019.03.004

Fig. 1.

Fig. 1.

Multi-city travel SIR model.

*Sci(t), Ici(t) and Rci(t) represent, respectively, the number of susceptible (S), infected (I) and recovered (R) people in city i at time t; β is the transmission rate; γ is the recovery rate; ΔSciI(t), ΔIciI(t) and ΔRciI(t) represent, respectively, the variations in S, I and R caused by infection in city i at time t; ΔSciM(t), ΔIciM(t) and ΔRciM(t) represent, respectively, the variations in S, I and R caused by human mobility at time t; nc is the total number of cities; jij=1ncScjci(t), jij=1ncIcjci(t) and jij=1ncRcjci(t) represent, respectively, the S, I and R inflows from other cities to city i at time t; and jij=1ncScicj(t), jij=1ncIcicj(t) and jij=1ncRcicj(t) represent, respectively, the S, I and R outflows from city i to other cities at time t.