Mathematical Models for Infectious Disease Transmission with Stochastic Simulation of Measles Outbreaks

As they are the leading cause of death among children and adolescents worldwide, it is of extreme importance to control the spread of infectious diseases. Information gained from mathematical modeling of these events often proves quite useful in establishing policy decisions to accomplish this goal. Human behavior, however, is quite difficult to recreate when using equations with pre-determined results, such as deterministic differential equations often used with epidemic models. Because of this, the focus of the research was to create a simulation of an outbreak, specifically of measles, by using an imaginary population experiencing simulated stochastic events on a discrete time scale. This allows us to model a more complex population, which includes various levels of immunization as well as different stages of infection. Another major factor that the program accounts for is the phenomenon of self-quarantine during a disease outbreak. An important supplement to mathematical analysis, the results from the program may provide new insight on dynamics of epidemics such as herd immunity and effective disease transmission