Computational modelling through the use of gPROMS

The question involves the use gPROMS as a programming language to solve a mathematical/engineering question. All inputs and outputs must be included so I know that the code works.

Computational modelling can be used to predict the transmission of infectious diseases (such as,
pandemic influenza, Ebola transmission, Zika transmission) and guide the public health policy.
Consider Fig. 2 and the following compartmental model (Roosa and Chowell, 2019) of the 1918
influenza pandemic in San Francisco, California, given by the system of simultaneous Ordinary
Differential Equations (ODEs):
ds
-=-B.S.
dt
să
de
= B.S.
-k. E
d/
=k. E-y.
dt
dR
= y.1
dt
dc
dt
= k. E
where N is the total population size. The population can be considered to consist of 4 classes, S, E, I
and R, denoting the numbers of susceptible, exposed, infectious and recovered individuals, respectively,
and N = S + E + I + R. The constant parameters in the model are denoted by B, k and y, where the
nominal values of the parameters are:
B = 0.56
1
k=
1.9
1
Y=
4.1
Part A: Simulation: Assume that N = 500000. Simulate the ODE model using gPROMS for S(O)=1(0)
=N/2, E(0) = R(O) = C(0) = 0 and 1 = [0, 17], and plot the state and auxiliary variables, i.e., S, E, I, R
and C, as a function of t.
[25]
Part B: There is an uncertainty of +10% from the reported nominal values of the constant parameters,
B, k and y. Simulate the ODE model in Part A for some variations (to be selected by you) in the values
of the constant parameters from their nominal values and report the effect of these variations on the
state and auxiliary variables. Plot the state and auxiliary variables as a function of 1 for some selected
values of the constant parameters.
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From: Assessing parameter identifiability in compartmental dynamic models using a computational
approach: application to infectious disease transmission models
BI(t)
N
Y
S
E
R
K
С
Fig. 2. Simple SEIR – Population is divided into 4 classes: susceptible (S), exposed (E), infectious (1),
and recovered/removed (R). Class C represents the auxiliary variable C(t) and tracks the cumulative
number of infectious individuals from the start of the outbreak. This is presented as a dashed line, as it
is not a state of the system of equations, but simply a class to track the cumulative incidence cases;