Chapter 21
Infectious Diseases
The endemic and epidemic diseases in Scotland fall chiefly, as is
usual, on the poor.
(Thomas Malthus, 1798)
21.1 Basic Epidemic Model
In this model we consider the spread of an infectious disease within a population.
We assume that there is some initial number of individuals already infected with the
disease. These individuals can pass on the disease to a group of susceptibles S. We
do not model explicitly the agents that cause the disease, such as viruses or bacteria.
Doing that would be rather impractical if we would want to apply our model to real
world diseases. Tracing the billions of agents that can cause the outbreak with a
particular disease is virtually impossible. Therefore, we do not explicitly model the
dynamics of individuals in a population of disease-causing agents but deal with
their effects in an aggregate way.
The law of mass action discussed in Part II of this book has proven to be a
powerful analogous way of capturing the spread of a disease in a population. The two
“reactants” in our case are the susceptible individuals S and the infective ones I. We
define a contact rate BETA at which these two groups of individuals make contact
and propagate the disease. This contact rate BETA is analogous to the reaction rates
in chemical reactions.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_21,
© Springer International Publishing Switzerland 2014
167
Infectious Diseases
The endemic and epidemic diseases in Scotland fall chiefly, as is
usual, on the poor.
(Thomas Malthus, 1798)
21.1 Basic Epidemic Model
In this model we consider the spread of an infectious disease within a population.
We assume that there is some initial number of individuals already infected with the
disease. These individuals can pass on the disease to a group of susceptibles S. We
do not model explicitly the agents that cause the disease, such as viruses or bacteria.
Doing that would be rather impractical if we would want to apply our model to real
world diseases. Tracing the billions of agents that can cause the outbreak with a
particular disease is virtually impossible. Therefore, we do not explicitly model the
dynamics of individuals in a population of disease-causing agents but deal with
their effects in an aggregate way.
The law of mass action discussed in Part II of this book has proven to be a
powerful analogous way of capturing the spread of a disease in a population. The two
“reactants” in our case are the susceptible individuals S and the infective ones I. We
define a contact rate BETA at which these two groups of individuals make contact
and propagate the disease. This contact rate BETA is analogous to the reaction rates
in chemical reactions.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_21,
© Springer International Publishing Switzerland 2014
167