7 research outputs found

    Dynamics of a stochastic epidemic model with quarantine and non-monotone incidence

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    In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts

    Modeling and analysis of SIR epidemic dynamics in immunization and cross-infection environments: Insights from a stochastic model

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    We propose a stochastic SIR model with two different diseases cross-infection and immunization. The model incorporates the effects of stochasticity, cross-infection rate and immunization. By using stochastic analysis and Khasminski ergodicity theory, the existence and boundedness of the global positive solution about the epidemic model are firstly proved. Subsequently, we theoretically carry out the sufficient conditions of stochastic extinction and persistence of the diseases. Thirdly, the existence of ergodic stationary distribution is proved. The results reveal that white noise can affect the dynamics of the system significantly. Finally, the numerical simulation is made and consistent with the theoretical results

    Survival analysis and probability density function of switching heroin model

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    We study a switching heroin epidemic model in this paper, in which the switching of supply of heroin occurs due to the flowering period and fruiting period of opium poppy plants. Precisely, we give three equations to represent the dynamics of the susceptible, the dynamics of the untreated drug addicts and the dynamics of the drug addicts under treatment, respectively, within a local population, and the coefficients of each equation are functions of Markov chains taking values in a finite state space. The first concern is to prove the existence and uniqueness of a global positive solution to the switching model. Then, the survival dynamics including the extinction and persistence of the untreated drug addicts under some moderate conditions are derived. The corresponding numerical simulations reveal that the densities of sample paths depend on regime switching, and larger intensities of the white noises yield earlier times for extinction of the untreated drug addicts. Especially, when the switching model degenerates to the constant model, we show the existence of the positive equilibrium point under moderate conditions, and we give the expression of the probability density function around the positive equilibrium point

    Estudio del efecto de la vacunaci贸n en modelos de epidemias con transmisi贸n estoc谩stica

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    Tesis in茅dita de la Universidad Complutense de Madrid, Facultad de Estudios Estad铆sticos, le铆da el 15-12-2022Mathematical epidemic models are frequently used in biology for analyzing transmission dynamics of infectious diseases and assessing control measures to interrupt their expansion. In order to select and develop properly the above mathematical models, it is necessary to take into account the particularities of an epidemic process as type of disease, mode of transmission and population characteristics. In this thesis we focus on infectious diseases with stochastic transmission including vaccination as a control measure to stop the spread of the pathogen. To that end, we consider constant and moderate size populations where individuals are homogeneously mixed. We assume that characteristics related to the transmission/recovery of the infectious disease present a common probabilistic behavior for individuals in the population. To assure herd immunity protection, we consider that a percentage of the population is protected against the disease by a vaccine, prior to the start of the outbreak.The administered vaccine is imperfect in the sense that some individuals, who have been previously vaccinated, failed to increase antibody levels and, in consequence, they could be infected. Pathogenic transmission occurs by direct contact with infected individuals. As population is not isolated, disease spreads from direct contacts with infected individuals inside or outside the population...Los modelos matem谩ticos epidemiol贸gicos se usan frecuentemente en biolog铆a para analizar las din谩micas de transmisi贸n de enfermedades infecciosas y para evaluar medidas de control con el objetivo de frenar su expansi贸n. Para poder seleccionar y desarrollar adecuadamente estos modelos es necesario tener en cuenta las particularidades propias del proceso epid茅mico tales como el tipo de enfermedad, modo de transmisi贸n y caracter铆sticas de la poblaci贸n. En esta tesis nos centramos en el estudio de enfermedades de tipo infeccioso con transmisi贸n por contacto directo, que disponen de una vacuna como medida de contenci贸n en la propagaci贸n del pat贸geno. Para ello, consideramos poblaciones de tama帽o moderado, que permanece constante a lo largo de un brote y asumiremos que los individuos no tienen preferencia a la hora de relacionarse y que las caracter铆sticas referentes a la transmisi贸n de la enfermedad se representan en t茅rminos de variables aleatorias, comunes para todos los individuos. La poblaci贸n no est谩 aislada y la transmisi贸n del pat贸geno se produce mediante contacto directo con cualquier persona infectada, tanto de dentro de la poblaci贸n como fuera de ella. Asumimos que, antes del inicio del brote epid茅mico, se ha administrado la vacuna a un porcentaje suficiente de individuos de la poblaci贸n, de forma que se asegure la inmunidad de reba帽o. Consideramos que la vacuna administrada es imperfecta en el sentido que algunos individuos vacunados no logran desarrollar anticuerpos frente a la enfermedad y por lo tanto, podr铆an resultar infectados al contactar con individuos enfermos...Fac. de Estudios Estad铆sticosTRUEunpu

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