Simple Problem

For a simple problem, we consider the SIR model defined by

\[\begin{split}\frac{dS}{dt} &= -\beta SI \\ \frac{dI}{dt} &= \beta SI - \gamma I \\ \frac{dR}{dt} &= \gamma I.\end{split}\]

which consists of two transitions

Let’s define this using the code block below

In [1]: from pygom import SimulateOde, Transition, TransitionType

In [2]: ode1 = Transition(origin='S', equation='-beta*S*I', transition_type=TransitionType.ODE)

In [3]: ode2 = Transition(origin='I', equation='beta*S*I - gamma*I', transition_type=TransitionType.ODE)

In [4]: ode3 = Transition(origin='R', equation='gamma*I', transition_type=TransitionType.ODE)

In [5]: stateList = ['S', 'I', 'R']

In [6]: paramList = ['beta', 'gamma']

In [7]: ode = SimulateOde(stateList,
   ...:                   paramList,
   ...:                   ode=[ode1, ode2, ode3])
   ...: 

In [8]: ode.get_transition_matrix()
Out[8]: 
Matrix([
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]])

and the last line shows that the transition matrix is empty. This is the expected result because SimulateOdeModel was not initialized using transitions. We populate the transition matrix below and demonstrate the difference.

In [9]: ode = ode.get_unrolled_obj()

In [10]: ode.get_transition_matrix()
Out[10]: 
Matrix([
[0, I*S*beta,       0],
[0,        0, I*gamma],
[0,        0,       0]])