ABSTRACT
An SIR epidemic model is analysed with respect to the identification of its parameters and initial values, based upon reported case data from public health sources. The objective of the analysis is to understand the relationship of unreported cases to reported cases. In many epidemic diseases the reported cases are a small fraction of the unreported cases. This fraction can be estimated by the identification of parameters for the model from reported case data. The analysis is applied to the Hong Kong seasonal influenza epidemic in New York City in 1968-1969.
Subject(s)
Epidemics/statistics & numerical data , Models, Biological , Basic Reproduction Number/statistics & numerical data , Computational Biology , Disease Susceptibility , Epidemics/history , History, 20th Century , Humans , Influenza, Human/epidemiology , Influenza, Human/history , Influenza, Human/transmission , Mathematical Concepts , New York City/epidemiologyABSTRACT
Salmonellosis is a foodborne disease of humans and animals caused by infection with Salmonella. The aim of this paper is to improve a deterministic model (DM) and an individual-based model (IBM) with reference to Salmonella propagation in flocks of laying hens taking into account variations in hens housed in the same cage and to compare both models. The spatio-temporal evolution, the basic reproduction number, R 0, and the speed of wave propagation were computed for both models. While in most cases the DM allows summary of all the features of the model in the formula for computation of R 0, slight differences between individuals or groups may be observed with the IBM that could not be expected from the DM, especially when initial environmental contamination is very low and some cages may get rid of bacteria. Both models suggest that the cage size plays a role on the risk and speed of propagation of the bacteria, which should be considered when designing new breeding systems.
Subject(s)
Chickens/microbiology , Housing, Animal , Poultry Diseases/epidemiology , Salmonella Infections, Animal/epidemiology , Animals , Female , Models, Statistical , Poultry Diseases/microbiology , Poultry Diseases/transmission , Prevalence , Salmonella Infections, Animal/transmissionABSTRACT
The main purpose of this article is to formulate a deterministic mathematical model for the transmission of malaria that considers two host types in the human population. The first type is called "non-immune" comprising all humans who have never acquired immunity against malaria and the second type is called "semi-immune". Non-immune are divided into susceptible, exposed and infectious and semi-immune are divided into susceptible, exposed, infectious and immune. We obtain an explicit formula for the reproductive number, R(0) which is a function of the weight of the transmission semi-immune-mosquito-semi-immune, R(0a), and the weight of the transmission non-immune-mosquito-non-immune, R(0e). Then, we study the existence of endemic equilibria by using bifurcation analysis. We give a simple criterion when R(0) crosses one for forward and backward bifurcation. We explore the possibility of a control for malaria through a specific sub-group such as non-immune or semi-immune or mosquitoes.