4.1. Basic Model
55
Although this chapter does not explicitly deal with the causes of anthropogenic stress, it does provide the framework to model the spread of a disease in a population and to trace impacts of a disease on population dynamics. The physical and biotic environment are held constant. Later
chapters deal with a varying environment, and we encourage you to revisit
the following epidemics models to include the effects of environmental
variability on the different subpopulations of susceptible, infected and immune individuals .
4.1. Basic Model
Let us consider the simplified case in which the rate of reproduction of a
population is equal to its natural mortality rate. With this assumption we
have a steady-state population size. We are now able to focus on the effects of an epidemic itself on a population without having to model the
"normal" population dynamics-those dynamics that would prevail if the
disease were not present. However, if some individuals contract the disease , the population may experience an elevated mortality rate.
Let us distinguish three groups of individuals in the population. The first
includes individuals who are susceptible to a disease. The second group
contains individuals who are already infected with the disease . Their interaction with members of the susceptibles leads to the spread of the disease .
The third group contains individuals who have been infected with the disease , but have temporarily become immune. We don 't need to model individuals who have contracted the disease but died because they leave the
system and consequently don 't affect its dynamics.
Since we distinguish in our model three subpopulations, we need three
distinct stocks to keep track of their respective fates. Layout the model by
first identifying the stocks of SUSCEPTIBLE, INFECTED and IMMUNE individuals, and then make the connections between them as shown in Figure
4.1. The susceptible individuals become sick, then immune, then susceptible again .
Next assume there are an initial 1990 susceptible individuals, 10 infected
one s and no immune ones in the population. Also assume that it takes 3
weeks for sick individuals to become immune, and once immune they stay
immune for 20 weeks. Specify the initial value for the SUSCEPTIBLE stock
as we have done in the previous chapters. Then double-click on the stock
that captures the INFECTED portion of the population, and specify it as a
conveyor by check ing the respective box in the dialog box (Figure 4.2). A
conveyor functions much like a conveyor belt-individual units get placed
on the conveyor and then move for a specified time before they exit it
again . Specify a "Transit time" of 3 for our conveyor and an initial value of
l0-these are the 10 infected individuals, and they stay infected, like everyone else who enters the conveyor, for 3 weeks. Exit the dialog box by
55
Although this chapter does not explicitly deal with the causes of anthropogenic stress, it does provide the framework to model the spread of a disease in a population and to trace impacts of a disease on population dynamics. The physical and biotic environment are held constant. Later
chapters deal with a varying environment, and we encourage you to revisit
the following epidemics models to include the effects of environmental
variability on the different subpopulations of susceptible, infected and immune individuals .
4.1. Basic Model
Let us consider the simplified case in which the rate of reproduction of a
population is equal to its natural mortality rate. With this assumption we
have a steady-state population size. We are now able to focus on the effects of an epidemic itself on a population without having to model the
"normal" population dynamics-those dynamics that would prevail if the
disease were not present. However, if some individuals contract the disease , the population may experience an elevated mortality rate.
Let us distinguish three groups of individuals in the population. The first
includes individuals who are susceptible to a disease. The second group
contains individuals who are already infected with the disease . Their interaction with members of the susceptibles leads to the spread of the disease .
The third group contains individuals who have been infected with the disease , but have temporarily become immune. We don 't need to model individuals who have contracted the disease but died because they leave the
system and consequently don 't affect its dynamics.
Since we distinguish in our model three subpopulations, we need three
distinct stocks to keep track of their respective fates. Layout the model by
first identifying the stocks of SUSCEPTIBLE, INFECTED and IMMUNE individuals, and then make the connections between them as shown in Figure
4.1. The susceptible individuals become sick, then immune, then susceptible again .
Next assume there are an initial 1990 susceptible individuals, 10 infected
one s and no immune ones in the population. Also assume that it takes 3
weeks for sick individuals to become immune, and once immune they stay
immune for 20 weeks. Specify the initial value for the SUSCEPTIBLE stock
as we have done in the previous chapters. Then double-click on the stock
that captures the INFECTED portion of the population, and specify it as a
conveyor by check ing the respective box in the dialog box (Figure 4.2). A
conveyor functions much like a conveyor belt-individual units get placed
on the conveyor and then move for a specified time before they exit it
again . Specify a "Transit time" of 3 for our conveyor and an initial value of
l0-these are the 10 infected individuals, and they stay infected, like everyone else who enters the conveyor, for 3 weeks. Exit the dialog box by