Creating a Model World
Sixth annual Clinic on Meaningful Modeling of Epidemiological Data
June 1-12, 2015, African Institute for Mathematical Sciences, Muizenberg, Cape Town, RSA
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In this exercise, participants go through a series of steps designed to help them develop a simplified conceptual model of their study system that will help them clarify and address their research question.
- Download slides with steps
- Once you have developed your diagram on paper, you may use this file as a template for creating a digital version of your diagram.
- Bring a hard copy of your diagram with you to Saturday’s 9am session.
Can Eastern red fox populations maintain rabies virus transmission?
Model world description
Susceptible foxes enter the population through birth, and the rate at which foxes are born varies seasonally and as a function of how many uninfected (susceptible) adult foxes are in the population at a given time. Juvenile foxes age into the adult class, on average $1/\psi$ time units after they are born. Both juveniles and adults can be infected by infectious foxes, and susceptible foxes experience a force of infection proportional to the prevalence of infectious foxes in the population. Once infected, foxes enter the exposed class. The incubation period is $1/\gamma$ time units (on average), after which the animals develop rabies, which is equivalent to transitioning from the exposed class to the infectious class. All foxes in the population experience background mortality with hazard $\mu$, and infectious foxes experience an additional disease-induced hazard of mortality, $\alpha$.
How would the existence of asymptomatic infections affect the trajectory of the Ebola epidemic in West Africa?
Steps for creating a model world
Identify the key outcome of interest for addressing your question. There may be multiple outcomes that you are interested in, but for now pick one primary outcome (such as the number of deaths per year, the incidence of infection, the presence or absence of the disease, etc).
Identify the processes that may affect the outcome of interest. This is a brainstorming step, and you should not worry about how important these processes are nor should you wrack your brain to make sure you identify every possible process that might be involved.
Identify relevant characteristics of individuals in your study system. These could be categorical (eg, male/female) or continuous (eg, age), and you should use your study question as a guide to the best way to describe continuous characteristics (eg, by exact age vs categories such as child/adult). This step is also a brainstorming step - write down whatever comes to mind.
Identify what you think are the most important processes and characteristics among those identified above for addressing your research question. If you are unable to select only a subset of the processes and characteristics identified, you are probably trying to understand too much all at once. Identify a smaller research question that will help inform the answer to your broad research question. For example, instead of asking how something occurs, you may pick a particular component that may be part of how something occurs and ask whether (and when) it can ever sufficiently explain the phenomenon of interest on its own.
Reconcile your process and characteristic lists by identifying how the most important processes relate to the most important characteristics. If you are missing any categories of individuals necessary to complete the important processes, or have categories that aren’t related to others through any of the listed processes, adjust your lists.
- Construct a diagram that represents all of the individual characteristics and processes of interest.
- For your own purposes, you can use whatever graphical conventions work best for how you think about the system.
- Hand draw or print a clean, clearly labeled version of your model diagram and bring it with you to tomorrow morning’s session.
- The physical (paper) version of your diagram, which you should bring with you on Thursday morning, should use arrows to represent the transitions from one category or state to another, and these transition arrows should be labeled with descriptions of what variables or other factors will influence the rate at which the transition occurs.
- If you use any letters or symbols in your diagram (chances are you will!), include a key that clearly state what each symbol/letter/abbreviation means.