16.4.1 Compartmental Model

A compartmental model is a form of mathematical model wherein simulation is

carried out to analyze interaction between individuals in different “compartments.”

Here, it is assumed that the people (or animal) in each compartment are same as all

the other people (or animals) in that compartment. These compartments could

(Bassingthwaighte 2012) either flow between each other or they could interact

with each other, and these rates of flow as well as interaction rates between

compartments may be taken as “parameters” of the model ascertained from obser-

vational studies of the species which could, in turn, estimate the average lifetime of

the species. One example is the finite element analysis model used in engineering

and biomedical engineering where an object is divided into small representative bits

to carry out an analysis of the changing forces on each element as the object moves.

The whole idea is to get a model which could simulate the reality and accordingly

vary those parameters to examine “alternate realities.” Finally, it could be used to

devise improved disease intervention strategies and other situations like optimizing

pest control, optimizing fisheries, etc.

Compartmental models prove to be very effective in carrying out simulation of

the spread of disease in a population. These models give us deep understanding of

the mechanisms and subtleties of the spread of disease (specifically when compari-

son is carried out with epidemic data). This, in turn, would help us develop

intervention strategies which could be more effective in managing the diseases.

One could also easily employ these disease models to successfully forecast the

course of an epidemic or a pandemic. The support parameters of compartmental

disease models are the “Susceptible” (S), “Infected” (I), and “Recovered”

(R) variables developed by Kermack and McKendrick (1927). The SIR model is a

basic form of compartmental model which works very efficiently for several diseases

including mumps, rubella, measles, influenza, etc. Many researchers have success-

fully made use of SIR model to analyze the propagation of COVID-19 pandemic and

predict its future course.

The models could be described either by employing deterministic ordinary

differential equations or with the help of more realistic but complicated stochastic

(random) framework. Models can easily predict disease spreads, epidemic duration,

and the total number infected, and also it can evaluate epidemiological parameters

such as the reproductive number. Such models could also be used to demonstrate the

effect of outcome of different public health interventions in an epidemic. For

example, it can help us decide for most efficient technique of distributing a limited

number of vaccines to a given population.

The physiological system under consideration could be divided into number of

interacting compartments in order to study its dynamic processes. Such a compart-

ment could be considered as a chemical species in a physical place with a uniformly

distributed tracer. In a given compartmental model:

•

Within the tissue of interest, an injected isotope would be present in a well-

defined number of interconnected physical or chemical states.

280

K. Tankeshwar and S. Srivastava