This paper considers the classical SIR epidemic model driven by a multidimensional Levy jump process. We consecrate to develop mathematical method obtain asymptotic properties of perturbed model. Our differs from previous approaches use comparison theorem, mutually exclusive possibilities lemma, and some new techniques stochastic differential systems. In this framework, we derive threshold whic...

Treatment is of great importance in fighting against infectious diseases. Backward bifurcation of SIR epidemic model with treatment rate is proposed and analyzed by Wang W. We have reinvestigated the above model by considering a backward bifurcation of SIR epidemic model with non-monotone incidence rate under treatment. It is assumed that the treatment rate is proportional to the number of pati...

We investigate the role of global mixing in epidemic processes. We first construct a simplified model of the SIR epidemic using a realistic population distribution. Using this model, we examine possible mechanisms for destruction of spatial correlations, in an attempt to produce correlation curves similar to those reported recently for real epidemiological data. We find that introduction of a l...

in this paper at rst, a history of mathematical models is given.next, some basic information about random variables, stochastic processesand markov chains is introduced. as follows, the entropy for a discrete timemarkov process is mentioned. after that, the entropy for sis stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

We study the statistical properties of the SIR epidemics in heterogeneous networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size sc. Using percolation theory to calculate the average fractional size 〈MSIR〉 of an epidemic, we find that the strength of the spanning link percolation cluster P∞ is an upper bound to 〈MSIR〉. For small values of sc, P∞...

We investigate the role of global mixing in epidemic processes. We first construct a simplified model of the SIR epidemic using a realistic population distribution. Using this model, we examine possible mechanisms for destruction of spatial correlations, in an attempt to produce correlation curves similar to those reported recently for real epidemiological data. We find that introduction of a l...

In this paper we study some deterministic mathematical models that seek to explain the expansion of zika virus, as a viral epidemic, using published data for Brazil. SIR type models are proposed and validated using the epidemic data found, considering several aspects in the spread of the disease. Finally, we confirmed that the crucial epidemic parameter such as R0 is consistent with those previ...

Studies on how to model the interplay between diseases and behavioral responses (so-called coupled disease-behavior interaction) have attracted increasing attention. Owing to the lack of obvious clinical evidence of diseases, or the incomplete information related to the disease, the risks of infection cannot be perceived and may lead to inappropriate behavioral responses. Therefore, how to quan...

Abstract We derive a generalized Hamiltonian formalism for modified susceptible–infectious–recovered/removed (SIR) epidemic model taking into account the population V of vaccinated persons. The resulting SIRV is shown to admit three possible functionally independent Hamiltonians and hence associated Poisson structures. reduced case vanishing sector shows complete correspondence with known struc...

Super-spreading events for infectious diseases occur when some infected individuals infect more than the average number of secondary cases. Several super-spreading individuals have been identified for the 2003 outbreak of severe acute respiratory syndrome (SARS). We develop a model for superspreading events of infectious diseases, which is based on the outbreak of SARS. Using this model we desc...