I worked an example for a SIR model to show people in the ecology field how they can use mrgsolve for their ODE-based models.

1 Write the SIR model

library(mrgsolve)library(tidyverse)model <-'$PARAM B = 1/70, mu = 1/70, Beta = 400, gamma = 365/14$INIT S = 1-0.001-0.9, I = 0.001, R = 0.9$ODEdouble N = S+I+R;dxdt_S = B-Beta*S*I/N-mu*S;dxdt_I = Beta*S*I/N-(mu+gamma)*I;dxdt_R = gamma*I-mu*R;$TABLEdouble R0 = Beta/(mu+gamma);'

2 Compile and load

mod <-mcode("sir", model, end =30, delta =1/120)

Building sir ... done.

3 Simulate

mod %>%mrgsim() %>%plot(scales ="same")

out <-mrgsim(mod, output="df")ggplot(out, aes(S,I)) +geom_point()

4 Challenge

Explore the dynamics of the system for different values of the beta and b parameters by simulating and plotting trajectories as time series and in phase space (e.g., I vs. S). How the beta, B, and R0 related to the type of trajectories you get?