Abstract. We formulate a delayed SIR epidemic model by introducing a latent period into susceptible, and infectious individuals in incidence rate. This new reformulation provides a reasonable role of incubation period on the dynamics of SIR epidemic model. We show that if the basic reproduction number, denoted, R0, is less than unity, the diseasefree equilibrium is locally asymptotically stable...

This article presents the solution of fractional SIR epidemic model using Laplace residual power series method. We introduce in sense Caputo’s derivative; it is presented by three differential equations, which third one depends on first coupled equations. The method (LRPSM) implemented this research to solve proposed model, we present a form convergent expansion that converges rapidly exact one...

In this work, we revisit the basic reproduction rate R 0 definition for analysis of epidemic-non-epidemic phases describing the dynamics of the discrete stochastic version of the epidemic SIR model based on the Master Equation formalism. One shows that it is a very precise and efficient way to determine the epidemic threshold; using its most primitive concept, we can find exact results.

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae, that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of h...

Mathematical models of the spread epidemic diseases are studied, paying special attention to networks. We treat Susceptible-Infected-Recovered (SIR) model and Susceptible-Exposed-Infectious-Recovered (SEIR) described by differential equations. perform microscopic numerical simulations for corresponding on Comparing a random network scale-free infection, we emphasize role hubs in network. also p...