Introduction to disease models

Disease models simulate the progression and transmission of biological diseases to better understand disease processes, predict outcomes in particular contexts, and evaluate the impact of interventions such as diagnostic tests, treatments, or vaccines. Disease models are a valuable tool in designing effective disease control programs. Similar models can be applied to simulating biological processes such as pregnancy or nutrition to influence family planning or nutrition programs.

There are many different types of disease models and the appropriate model for a given context will depend on many factors:

• Available data and data quality
• Specific research or policy questions
• Complexity of the biological process
• Available compute resources

The content in this section describes the basics of three classes of disease models:

• Compartmental models
• Agent-based models (ABMs)
• Statistical models

There will also be links to additional resources for you to learn more about each of the model classes, and examples of different open-source models provided by IDM that you can use.

Reproductive number

One key value used to describe how a disease transmits through a population is its reproductive number. This value can be estimated through different mathematical models and can help understand the level of interventions needed to control the spread of the disease through a population.

In a fully susceptible population, the basic reproductive number \(R_0\) is the number of secondary infections generated by the first infectious individual over the course of the infectious period. \(R_0=S*L*\beta\) (where S = the number of susceptible hosts, L = length of infection, and \(\beta\) = transmissibility). When \(R_0 > 1\), disease will spread. It is essentially a measure of the expected or average outcome of transmission. The effective reproductive number takes into account non-susceptible individuals. This is the threshold parameter used to determine whether or not an epidemic will occur, and determines:

• The initial rate of increase of an epidemic (the exponential growth phase).
• The final size of an epidemic (what fraction of susceptibles will be infected).
• The endemic equilibrium fraction of susceptibles in a population (\(1/R_0\)).
• The critical vaccination threshold, which is equal to \(1-(1/R_0)\), and determines the number of people that must be vaccinated to prevent the spread of a pathogen.

Model comparison

The following table provides a brief comparison of the three model types to be discussed; please note that these are generalizations, and there are many models that can (a) overcome the listed disadvantages, or (b) do not have the listed advantages:

Model type	Model features	Advantages	Disadvantages	Example use case
Compartmental	Models populations Population divided into compartments (disease states) Everyone in a compartment is identical Can be deterministic or stochastic Mechanistic	Quickly evaluates disease dynamics Simple and fast to run Excellent building block/starting point to understand disease dynamics Can include waning immunity, vaccination, some demographic heterogeneity	Cannot include individual level heterogeneity Cannot create realistic contact networks Model becomes unwieldy when trying to account for detailed data or complex interventions	How many COVID-19 cases will there be in 1 year if there's 95% vaccination?
Agent-based	Models individuals Can assign properties to each agent (individual) Typically stochastic	Easy to account for variation in individual behavior or characteristics Can define contact networks Complex or realistic interventions can be easily applied	Computationally expensive Difficult to build/code, calibrate, and troubleshoot Requires detailed data to run May be difficult to understand emergent properties or how features interact (or "what's under the hood" Difficult to parameterize	What coverage of mass drug administration and bed net usage do we need in this location to reduce malaria cases by 85%?
Statistical	Models correlations between transmission drivers and outcomes May incorporate temporal correlations (e.g., time series analysis) in outcomes Typically stochastic, incorporating noise Does not include dynamic processes	Predictive relationships are transparent (e.g., "increase in factor N results in X% increase in outcome." Relatively easy to fit models to data, with lots of existing software packages Straightforward to interpret results and approaches are well-understood by the modeling community	Depletions in pool of susceptibles tends to be ignored, resulting in over-estimates of transmission intensity Often fail to incorporate knock-on impact of interventions (e.g., prevention of infection results in prevention of resulting secondary infections) Difficult to incorporate heteroskedasticity Similar to compartmental models, difficult to incorporate complex interventions or realistic contact networks	What is the correlation between the presence or absence of mask usage and the number of reported cases of COVID-19?