scholarly journals Stability Analysis of a Multigroup SEIR Epidemic Model with General Latency Distributions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Nan Wang ◽  
Jingmei Pang ◽  
Jinliang Wang
Keyword(s):  
Epidemic Model ◽  
Classical Method ◽  
Theoretic Approach ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Latency Distributions ◽  
The Given

The global stability of a multigroup SEIR epidemic model with general latency distribution and general incidence rate is investigated. Under the given assumptions, the basic reproduction numberℜ0is defined and proved as the role of a threshold; that is, the disease-free equilibriumP0is globally asymptotically stable ifℜ0≤1, while an endemic equilibriumP*exists uniquely and is globally asymptotically stable ifℜ0>1. For the proofs, we apply the classical method of Lyapunov functionals and a recently developed graph-theoretic approach.

scholarly journals Dynamics of a Diffusive Multigroup SVIR Model with Nonlinear Incidence

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Jinhu Xu ◽  
Yan Geng
Keyword(s):  
Reproduction Number ◽  
Classical Method ◽  
Reaction Diffusion ◽  
Theoretic Approach ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Special Case ◽  
Disease Free

In this paper, a multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence is investigated. We first establish the well-posedness of the model. Then, the basic reproduction number ℜ 0 is established and shown as a threshold: the disease-free steady state is globally asymptotically stable if ℜ 0 < 1 , while the disease will be persistent when ℜ 0 > 1 . Moreover, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, we established the global stability of the endemic equilibria for a special case.

scholarly journals Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ming-Tao Li ◽  
Gui-Quan Sun ◽  
Juan Zhang ◽  
Zhen Jin
Keyword(s):  
Classical Method ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Theoretic Approach ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Graph Theoretic ◽  
Indirect Transmission ◽  
Global Dynamic ◽  
Disease Free

For a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens,V. cholerae, are present. The basic reproduction numberℛ0is identified and global dynamics are completely determined byℛ0. It shows thatℛ0is a globally threshold parameter in the sense that if it is less than one, the disease-free equilibrium is globally asymptotically stable; whereas if it is larger than one, there is a unique endemic equilibrium which is global asymptotically stable. For the proof of global stability with the disease-free equilibrium, we use the comparison principle; and for the endemic equilibrium we use the classical method of Lyapunov function and the graph-theoretic approach.

scholarly journals Centered Polygonal Lacunary Graphs: A Graph Theoretic Approach to p-Sequences of Centered Polygonal Lacunary Functions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1021 ◽  
Author(s):  
Keith Sullivan ◽  
Drew Rutherford ◽  
Darin J. Ulness
Keyword(s):  
Three Dimensional ◽  
Special Role ◽  
Theoretic Approach ◽  
Scaling Properties ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Condensed Graphs ◽  
Dimensional Graph ◽  
Insight Into

This work is on the nature and properties of graphs which arise in the study of centered polygonal lacunary functions. Such graphs carry both graph-theoretic properties and properties related to the so-called p-sequences found in the study of centered polygonal lacunary functions. p-sequences are special bounded, cyclic sequences that occur at the natural boundary of centered polygonal lacunary functions at integer fractions of the primary symmetry angle. Here, these graphs are studied for their inherent properties. A ground-up set of planar graph construction schemes can be used to build the numerical values in p-sequences. Further, an associated three-dimensional graph is developed to provide a complementary viewpoint of the p-sequences. Polynomials can be assigned to these graphs, which characterize several important features. A natural reduction of the graphs original to the study of centered polygonal lacunary functions are called antipodal condensed graphs. This type of graph provides much additional insight into p-sequences, especially in regard to the special role of primes. The new concept of sprays is introduced, which enables a clear view of the scaling properties of the underling centered polygonal lacunary systems that the graphs represent. Two complementary scaling schemes are discussed.

A Graph-Theoretic Approach to Comparing and Integrating Genetic, Physical and Sequence-Based Maps

Genetics ◽  
2003 ◽  
Vol 165 (4) ◽  
pp. 2235-2247
Author(s):  
Immanuel V Yap ◽  
David Schneider ◽  
Jon Kleinberg ◽  
David Matthews ◽  
Samuel Cartinhour ◽  
...  
Keyword(s):  
Directed Graph ◽  
Source Material ◽  
Complete Picture ◽  
Theoretic Approach ◽  
Research Groups ◽  
Genome Coverage ◽  
Graph Theoretic ◽  
Novel Approach ◽  
Graph Theoretic Approach ◽  
Locus Order

AbstractFor many species, multiple maps are available, often constructed independently by different research groups using different sets of markers and different source material. Integration of these maps provides a higher density of markers and greater genome coverage than is possible using a single study. In this article, we describe a novel approach to comparing and integrating maps by using abstract graphs. A map is modeled as a directed graph in which nodes represent mapped markers and edges define the order of adjacent markers. Independently constructed graphs representing corresponding maps from different studies are merged on the basis of their common loci. Absence of a path between two nodes indicates that their order is undetermined. A cycle indicates inconsistency among the mapping studies with regard to the order of the loci involved. The integrated graph thus produced represents a complete picture of all of the mapping studies that comprise it, including all of the ambiguities and inconsistencies among them. The objective of this representation is to guide additional research aimed at interpreting these ambiguities and inconsistencies in locus order rather than presenting a “consensus order” that ignores these problems.

scholarly journals Study of the Concrete Production Process -A graph theoretic approach

2020 ◽  
Vol 1706 ◽  
pp. 012115
Author(s):  
P Sangeetha ◽  
M Shanmugapriya ◽  
R Sundareswaran ◽  
K Sowmya ◽  
S Srinidhi
Keyword(s):  
Production Process ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Concrete Production
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