Models of infection: person to person

When faced with a spreading infection, public health workers want to predict its path and severity so they can make decisions about vaccination strategies, quarantine policy, and the use of public health resources. This is true whether the pathogen´s dispersion is natural (for example, the spread of influenza in 1918) or deliberate (for example, the spread of anthrax via terrorism). Effective mathematical models can help us test a public health policy´s potential outcome and initiate an effective response. In this problem, we focus on a simplified model of the spread of an infection and develop some tools that lend insight into its behavior. To make our problem as easy as possible, we impose some rather artificial assumptions. Suppose we have nm patients in a hospital ward and that their beds are arranged as n rows of m beds. For convenience, we´ll let m be an even number. Suppose also that one of the patients, the one in bed m/2 in row [n/2], becomes infected and can infect any patient in a neighboring bed. How will this infection spread through the ward? The article presents a Markov model and a Monte Carlo simulation to solve this problem.