Matlab projects - Disease Spread
Introduction
Computational modeling is key to understanding the spread of infectious disease, which is crucial for prevention and treatment of epidemics. There are many different types of predictive mathematical models that simplify complex situations into a few main variables or compartments. This paper and the attached Matlab files will compare two different H1N1 Influenza pandemic disease predictive mathematical models. In 2009, Towers and Feng used what they called “a seasonally forced deterministic Susceptible, Infective, Recovered (SIR) model” (Towers and Feng). That same year, Gurevich utilized a formal kinetics model, similar to the Towers and Feng model but differed in some assumptions (Gurevich).
Daley and Gani trace the origins of epidemiology to John Graunt in 1662; with epidemiology being defined as the scientific study of disease and adverse health effects (Daley and Gani), as well as the modeling and treatment of these health problems. Epidemics are the rapid spread of an infectious disease throughout a population in a region in a short period of time (Green et al.). Once an epidemic spreads to multiple locations and affects large numbers of people it becomes a pandemic (Aschengrau, Boston University School of Public Health Boston Massachusetts Ann Aschengrau, & Seage). Given that there are innumerable factors that affect real life disease spread, assumptions (aka compartments), must be made to form the equations in epidemiological models in order for them to be useful.
Among the many epidemiological models that have been created are the deterministic SIR (which the Towers and Feng paper use), SEIR, SIS, Carrier State, and MSIR models which are only valid for large population sizes. Stochastic models rely on random variables and are therefore valid for smaller population sizes (Shrestha et al.). The validity of the model is affected by the type of model, the model’s proper application to the population and disease being studied, and the complexity of the model. Compartmental models such as the SIR are presupposed on the law of mass action, which holds that the rate of a reaction is proportional to the concentrations of the reactants (Corlan and Ross).
In real life situations models based on the law of mass action sometimes fail due to limitations caused by abstraction. The assumptions that form the compartments of models like the SIR require a certain homogeneity in the mixture of the populations. There are numerous factors that affect how susceptible a population is to a specific disease, and sometimes these factors can be folded into compartments that behave predictably. When they do not however, this could make the model invalid and require a more sophisticated set of assumptions in order to create a valid model.