Page - 122 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

122 4 SolvingOrdinaryDifferentialEquations Thenew,extendeddifferential equationswith theV quantitybecome S0 D ˇSI C R pS; (4.36) V 0 DpS; (4.37) I 0 DˇSI I; (4.38) R0 D I R: (4.39) Weshall refer to thismodelas theSIRVmodel. The new equation forV 0 poses no difficulties when it comes to the numerical method. InaForwardEuler schemewesimplyaddanupdate VnC1 DVnCp tSn : Theprogramneeds tostoreV.t/ inanadditionalarrayV, andtheplottingcommand must be extendedwithmore arguments to plot V versus t aswell. The complete code is found in thefileSIRV1.py. Using p D 0:0005 andp D 0:0001 as values for the vaccine efficiency pa- rameter, the effect of vaccination is seen in Fig. 4.13 (other parameters are as in Fig. 4.11). Fig.4.13 Theeffect ofvaccination:pD0:0005 (left)andpD0:0001 (right)