## Flow Diagrams

A key stage in the design and definition of a transmission dynamics model is preparation of a flow diagram. This comprises (1) a set of compartments representing that part of the population found in each of the various states of susceptibility, infection or disease to be included in the model and (2) the transitions or flows of population from one state to another upon initial infection, progression of disease, recovery etc. Such diagrams may often appear simple in the extreme (Figure 15.1), but they provide an invaluable aid to thinking about the epidemiological system being modeled by ensuring that the modeler specifies very precisely which stages of infection will be

Figure 15.1. A simple flow diagram. The diagram shows the compartments representing the susceptible (S), infected (I) and recovered (R) proportions of the population and arrows representing the flows or transitions between compartments upon infection, at rate X (the force of infection) per capita, and recovery from infection at the per capita rate a; arrows representing births into the population and deaths leaving the population may also be included if desired or useful. This is often referred to as an S-I-R model, although the letters X, Y and Z are commonly used in place, respectively, of S, I and R.

Figure 15.1. A simple flow diagram. The diagram shows the compartments representing the susceptible (S), infected (I) and recovered (R) proportions of the population and arrows representing the flows or transitions between compartments upon infection, at rate X (the force of infection) per capita, and recovery from infection at the per capita rate a; arrows representing births into the population and deaths leaving the population may also be included if desired or useful. This is often referred to as an S-I-R model, although the letters X, Y and Z are commonly used in place, respectively, of S, I and R.

incorporated in the model (and what, precisely, is the meaning of each stage), and also how each stage is entered and how it is left; this should be done bearing in mind that simplicity will facilitate understanding and that unnecessary complexity will have the opposite result.

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