Veterinary MedicineInfectious DiseasesEpidemiologyInfectious Disease EpidemiologyStochastic ProcessesDisease EpidemiologyDisease SpreadInfectious Disease DynamicsMicrobial Transmission DynamicsPopulation Dynamics ModelingTransmission DynamicsAsymptotic TheoryEpidemic ModelsInfectious Disease ModelsMathematical Modeling Of EpidemicsOrnstein-uhlenbeck ModelsOrnstein-uhlenbeck ProcessesPopulation SizeStochastic Epidemic Models
In the mathematical model for the simple epidemic, it is assumed that the population at time t consists of X(t) infectives and N-X(t) susceptibles, and the X(t) is a pure birth process with transition probabilities. There is quite an extensive literature devoted to the analysis of the process X(t). In this paper a valid asymptotic distribution theory for large values of N is developed and a simple efficient estimator of the infection rate lambda is derived. The author concluded with the analysis of a more general model for the simple epidemic in which the population is divided into a number of homogeneous groups. (Author)