Add incidence flag to SEIRModel.simulate method

[DavAug]

Looking at the exercise sheet, epidemiological models like the SEIR model are often used to simulate the number of infections in a given time unit (often days). At the moment we are just returning the states (S, E, I, R), but the incidence number is the influx to I from time t_i to t_f, say from Tuesday to Wednesday. To be able to return the number of incidences we have to slightly modify the simulate function.

• [x] Add an additional argument called return_incidence to simulate which by default assumes the value False.
• [x] Adjust the _right_hand_side method to additionally compute the incidence number (i.e. n_incidence which is called C on the exercise sheet) by just extending the states (S, E, I, R) to (S, E, I, R, n_incidence). The right hand side of n_incidence is

  dn_incidence / dt = kappa * E

• [x] If return_incidence is False, return the simulated S, E, I, R values as before.
• [x] If return_incidence is True, execute a private method _compute_incidences that returns the number of new cases between the provided times.

[DavAug]

As disussed it is probably best to avoid adding an additional state variable and compute n_incidence from I and R. For times = [t_0, t_1, ... , t_f] n_incidence can be computed as

total_infected = i + r
n_incidence = total_infected[1:] - total_infected[:-1]

i.e. [total_infected[t_1] - total_infected[t_0], [total_infected[t_2] - total_infected[t_1], ... ]