A Tale of Two Fields: Mathematical and Statistical Modeling of Infectious Diseases

The managing editor of Osong Public Health and Research Perspectives (PHRP) attended the Casablanca International Workshop in Mathematical Biology: Analysis and Control, Morocco, June 20e24, 2011. PHRP was welcomed by the community, especially by the infectious disease-modeling group. They welcomed a new public health journal that contains articles for applied mathematical modelers. It is an asset to have such strong supporters for PHRP. Mathematical models for public health experts are varied. The classical disease-transmission model was created by Kermack-McKendrick in 1927 [1]. In this model, disease transmission is conveniently conceptualized as passage among members of a population by moving among compartments. Actually, this is a special case of the Susceptible-Infectious-Removed (SIR) compartmentalmodel. SIR functionswell for infectious or communicable diseases with immunity against re-infection or disease with no immunity. Another model divides I-class into two classes with an exposed period between being infected and becoming infectious, which yields Susceptible-Exposed-Infectious-Removed (SEIR) and Susceptible-Exposed-Infectious-Susceptible (SEIS). We can consider Susceptible-Infectious-Removed-Susceptible (SIRS) models with temporary immunity [1]. In the simple Susceptible-Infected-Susceptible model, the deterministic dynamic structure shows us a great deal about the behavior of stochastic paths and brings to our attention questions that pertain to the stochastic model: What is the nature of the stochastic path as it varies near the deterministic equilibrium? Starting from the deterministic equilibrium, what is the distribution of time until the stochastic hits zero? We should point out that the stochastic models that we have discussed here are simple ones, involving no more than two linked stochastic equations [2]. The basic reproduction number R0 is the