The Experts below are selected from a list of 19275 Experts worldwide ranked by ideXlab platform

Daqing Jiang - One of the best experts on this subject based on the ideXlab platform.

  • threshold behaviour of a stochastic SIR Model
    Applied Mathematical Modelling, 2014
    Co-Authors: Daqing Jiang
    Abstract:

    Abstract In this paper, we investigate the threshold behaviour of a susceptible-infected-recovered (SIR) epidemic Model with stochastic perturbation. When the noise is small, we show that the threshold determines the extinction and persistence of the epidemic. Compared with the corresponding deterministic system, this value is affected by white noise, which is less than the basic reproduction number of the deterministic system. On the other hand, we obtain that the large noise will also suppress the epidemic to prevail, which never happens in the deterministic system. These results are illustrated by computer simulations.

  • long time behavior of a stochastic SIR Model
    Applied Mathematics and Computation, 2014
    Co-Authors: Daqing Jiang, Yuguo Lin, Peiyan Xia
    Abstract:

    Abstract In this paper, we analyze long-time behavior of densities of the distributions of the solution for a stochastic SIR epidemic Model. We prove that the densities can converge in L 1 to an invariant density or can converge weakly to a singular measure.

  • asymptotic behavior of global positive solution to a stochastic SIR Model
    Mathematical and Computer Modelling, 2011
    Co-Authors: Daqing Jiang, Ningzhong Shi
    Abstract:

    In this paper, we explore a stochastic SIR Model and show that this Model has a unique global positive solution. Furthermore, we investigate the asymptotic behavior of this solution. Finally, numerical simulations are presented to illustrate our mathematical findings.

  • global stability of two group SIR Model with random perturbation
    Journal of Mathematical Analysis and Applications, 2009
    Co-Authors: Daqing Jiang, Ningzhong Shi
    Abstract:

    Abstract In this paper, we discuss the two-group SIR Model introduced by Guo, Li and Shuai [H.B. Guo, M.Y. Li, Z. Shuai, Global stability of the endemic equilibrium of multigroup SIR epidemic Models, Can. Appl. Math. Q. 14 (2006) 259–284], allowing random fluctuation around the endemic equilibrium. We prove the endemic equilibrium of the Model with random perturbation is stochastic asymptotically stable in the large. In addition, the stability condition is obtained by the construction of Lyapunov function. Finally, numerical simulations are presented to illustrate our mathematical findings.

Lei Ying - One of the best experts on this subject based on the ideXlab platform.

  • information source detection in the SIR Model a sample path based approach
    IEEE ACM Transactions on Networking, 2016
    Co-Authors: Kai Zhu, Lei Ying
    Abstract:

    This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) Model. We assume all nodes in the network are in the susceptible state initially, except one single information source that is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know the graph topology and all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample-path-based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for g + 1-regular trees such that gq > 1, where g + 1 is the node degree and is the infection probability, the estimator is within a constant distance from the actual source with a high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic. We then further evaluate the performance of the reverse infection algorithm on several real-world networks.

  • information source detection in the SIR Model a sample path based approach
    Information Theory and Applications, 2013
    Co-Authors: Kai Zhu, Lei Ying
    Abstract:

    This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) Model. We assume all nodes in the network are in the susceptible state initially except the information source which is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample path based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for g-regular trees such that gq > 1, where g is the node degree and q is the infection probability, the estimator is within a constant distance from the actual source with high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic.

  • information source detection in the SIR Model a sample path based approach
    arXiv: Social and Information Networks, 2012
    Co-Authors: Kai Zhu, Lei Ying
    Abstract:

    This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) Model. We assume all nodes in the network are in the susceptible state initially except the information source which is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample path based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for $g$-regular trees such that $gq>1,$ where $g$ is the node degree and $q$ is the infection probability, the estimator is within a constant distance from the actual source with a high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic. We then further evaluate the performance of the reverse infection algorithm on several real world networks.

Alexei J Drummond - One of the best experts on this subject based on the ideXlab platform.

  • simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth death SIR Model
    Journal of the Royal Society Interface, 2014
    Co-Authors: Denise Kuhnert, Tanja Stadler, Timothy G Vaughan, Alexei J Drummond
    Abstract:

    The evolution of RNA viruses, such as human immunodeficiency virus (HIV), hepatitis C virus and influenza virus, occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible–infected–removed (SIR) Model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our birth–death SIR method to two viral datasets. First, five HIV type 1 clusters sampled in the UK between 1999 and 2003 are analysed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 1990s. The analysis of a hepatitis C virus genotype 2c dataset shows that the local epidemic in the Cordoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880 to 1920. The estimated time of epidemic peak is around 1970.

  • simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth death SIR Model
    arXiv: Populations and Evolution, 2013
    Co-Authors: Denise Kuhnert, Tanja Stadler, Timothy G Vaughan, Alexei J Drummond
    Abstract:

    The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible-infected-removed (SIR) Model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our Birth-Death SIR method (BDSIR) to two viral data sets. First, five human immunodeficiency virus type 1 clusters sampled in the United Kingdom between 1999 and 2003 are analyzed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 90's. The analysis of a hepatitis C virus (HCV) genotype 2c data set shows that the local epidemic in the C\'ordoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880--1920. The estimated time of epidemic peak is around 1970.

Timothy G Vaughan - One of the best experts on this subject based on the ideXlab platform.

  • simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth death SIR Model
    Journal of the Royal Society Interface, 2014
    Co-Authors: Denise Kuhnert, Tanja Stadler, Timothy G Vaughan, Alexei J Drummond
    Abstract:

    The evolution of RNA viruses, such as human immunodeficiency virus (HIV), hepatitis C virus and influenza virus, occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible–infected–removed (SIR) Model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our birth–death SIR method to two viral datasets. First, five HIV type 1 clusters sampled in the UK between 1999 and 2003 are analysed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 1990s. The analysis of a hepatitis C virus genotype 2c dataset shows that the local epidemic in the Cordoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880 to 1920. The estimated time of epidemic peak is around 1970.

  • simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth death SIR Model
    arXiv: Populations and Evolution, 2013
    Co-Authors: Denise Kuhnert, Tanja Stadler, Timothy G Vaughan, Alexei J Drummond
    Abstract:

    The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible-infected-removed (SIR) Model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our Birth-Death SIR method (BDSIR) to two viral data sets. First, five human immunodeficiency virus type 1 clusters sampled in the United Kingdom between 1999 and 2003 are analyzed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 90's. The analysis of a hepatitis C virus (HCV) genotype 2c data set shows that the local epidemic in the C\'ordoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880--1920. The estimated time of epidemic peak is around 1970.

Haiyan Wang - One of the best experts on this subject based on the ideXlab platform.

  • traveling wave phenomena in a kermack mckendrick SIR Model
    Journal of Dynamics and Differential Equations, 2016
    Co-Authors: Haiyan Wang, Xiangsheng Wang
    Abstract:

    We study the existence and nonexistence of traveling waves of a general diffusive Kermack–McKendrick SIR Model with standard incidence where the total population is not constant. The three classes, susceptible S, infected I and removed R, are all involved in the traveling wave solutions. We show that the minimum wave speed of traveling waves for the three-dimensional non-monotonic system can be derived from its linearizaion at the initial disease-free equilibrium. The proof in this paper is based on Schauder fixed point theorem and Laplace transform. Our study provides a promising method to deal with high dimensional epidemic Models.

  • traveling wave phenomena in a kermack mckendrick SIR Model
    arXiv: Analysis of PDEs, 2014
    Co-Authors: Haiyan Wang, Xiangsheng Wang
    Abstract:

    We study the existence and nonexistence of traveling waves of general diffusive Kermack-McKendrick SIR Models with standard incidence where the total population is not constant. The three classes, susceptible $S$, infected $I$ and removed $R$, are all involved in the traveling wave solutions. We show that the minimum speed for the existence of traveling waves for this three-dimensional non-monotonic system can be derived from its linearizaion at the initial disease-free equilibrium. The proof in this paper is based on Schauder fixed point theorem and Laplace transform and provides a promising method to deal with high dimensional epidemic Models.