Modeling and Analysis of the Multiannual Cholera Outbreaks with Host-Pathogen Encounters

2020 ◽  
Vol 30 (08) ◽  
pp. 2050120
Author(s):  
Wenjing Zhang
Keyword(s):  
Complex Dynamics ◽  
Backward Bifurcation ◽  
Global Dynamics ◽  
Modeling And Analysis ◽  
Local And Global Dynamics ◽  
Model Dynamics ◽  
Host Pathogen ◽  
Necessary And Sufficient ◽  
And Control ◽  
Parameter Values

Re-emergence of cholera threatens people’s health globally. However, its periodic re-emerging outbreaks are still poorly understood. In this paper, we develop a simple ordinary differential equation (ODE) model to study the cholera outbreak cycles. Our model involves both direct (i.e. human-to-human) and indirect (i.e. environment-to-human) transmission routes, due to the multiple interactions between the human host, the pathogen, and the environment. In particular, we model the pathogen searching distance as a Poisson point process, and then formulate the host-pathogen encounter (HPE) rate. A thorough mathematical analysis is performed to investigate local and global dynamics of the model. Necessary and sufficient condition under which the backward bifurcation occurs is derived. Fold, Hopf, and Bogdanov–Takens bifurcations are studied with original model parameter values to reveal their relations with model behaviors. One- and two-dimensional bifurcation diagrams are provided to categorize model dynamics with respect to its parameter values. Analytical and numerical analyses show that our simple model is sufficient to exhibit complex epidemic patterns of cholera dynamics including bistability and annual and multiannual periodic outbreaks. Our result regarding the backward bifurcation and complex dynamics of cholera epidemics highlight the challenges in the prevention and control of the disease.

scholarly journals Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1458 ◽  
Author(s):  
Sameh S Askar ◽  
Abdulrahman Al-Khedhairi
Keyword(s):  
Complex Dynamics ◽  
Market Competition ◽  
Equilibrium Points ◽  
Profit Maximization ◽  
Stable Complex ◽  
Global Dynamics ◽  
Limited Information ◽  
Critical Curves ◽  
Local And Global Dynamics ◽  
Realistic Situation

The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained.

Complex Dynamics in a Model of Common Fishery Resource Harvested by Multiagents with Heterogeneous Strategy

2015 ◽  
Vol 25 (11) ◽  
pp. 1550153 ◽  
Author(s):  
En-Guo Gu
Keyword(s):  
Complex Dynamics ◽  
Sustainable Use ◽  
Fish Stock ◽  
Global Dynamics ◽  
Coexisting Attractors ◽  
Fishery Resource ◽  
Local Bifurcations ◽  
Local And Global Dynamics ◽  
Strategic Behaviors ◽  
Special Case

In this paper, we formulate a dynamical model of common fishery resource harvested by multiagents with heterogeneous strategy: profit maximizers and gradient learners. Special attention is paid to the problem of heterogeneity of strategic behaviors. We mainly study the existence and the local stability of non-negative equilibria for the model through mathematical analysis. We analyze local bifurcations and complex dynamics such as coexisting attractors by numerical simulations. We also study the local and global dynamics of the exclusive gradient learners as a special case of the model. We discover that when adjusting the speed to be slightly high, the increasing ratio of gradient learners may lead to instability of the fixed point and makes the system sink into complicated dynamics such as quasiperiodic or chaotic attractor. The results reveal that gradient learners with high adjusting speed may ultimately be more harmful to the sustainable use of fish stock than the profit maximizers.

Effect of pollution on dynamics of SIR model with treatment

2015 ◽  
Vol 08 (06) ◽  
pp. 1550083 ◽  
Author(s):  
Sudipa Chauhan ◽  
Sumit Kaur Bhatia ◽  
Surbhi Gupta
Keyword(s):  
Reproduction Number ◽  
Sir Model ◽  
Backward Bifurcation ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Disease Eradication ◽  
Sir Epidemic ◽  
Local And Global Dynamics ◽  
High Level ◽  
Very High

In this paper, an SIR epidemic model with treatment affected by pollution is proposed. The existence, local and global dynamics of the model are studied. It is shown that backward bifurcation occurs at R0 < 1 and p0 < 1 because of insufficient capacity of treatment. It is also found that due to pollution the number of infective has gone to a very high level. As a result, backward bifurcation occurs for R0 < 1, even when p0 > 1. Further, there exist bistable endemic equilibria for a very low capacity for R0 > 1. Thus, we found that disease can be eradicated for R0 < 1 only by increasing the capacity to a sufficiently high level. Persistence of endemicity of the system is obtained and the mathematical results suggest that the basic reproduction number is insufficient for disease eradication. Numerical simulations are presented to illustrate the results obtained.

scholarly journals Subgraphs of Interest Social Networks for Diffusion Dynamics Prediction

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 492
Author(s):  
Valentina Y. Guleva ◽  
Polina O. Andreeva ◽  
Danila A. Vaganov
Keyword(s):  
Social Networks ◽  
Sampling Method ◽  
Building Blocks ◽  
Global Dynamics ◽  
Diffusion Dynamics ◽  
Different Types ◽  
Prediction And Control ◽  
Path Lengths ◽  
And Control ◽  
Diffusion Prediction

Finding the building blocks of real-world networks contributes to the understanding of their formation process and related dynamical processes, which is related to prediction and control tasks. We explore different types of social networks, demonstrating high structural variability, and aim to extract and see their minimal building blocks, which are able to reproduce supergraph structural and dynamical properties, so as to be appropriate for diffusion prediction for the whole graph on the base of its small subgraph. For this purpose, we determine topological and functional formal criteria and explore sampling techniques. Using the method that provides the best correspondence to both criteria, we explore the building blocks of interest networks. The best sampling method allows one to extract subgraphs of optimal 30 nodes, which reproduce path lengths, clustering, and degree particularities of an initial graph. The extracted subgraphs are different for the considered interest networks, and provide interesting material for the global dynamics exploration on the mesoscale base.

scholarly journals Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Serena Brianzoni ◽  
Cristiana Mammana ◽  
Elisabetta Michetti
Keyword(s):  
Production Function ◽  
Growth Model ◽  
Discrete Time ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Global Dynamics ◽  
Production Factors ◽  
Local And Global Dynamics ◽  
Complex Features

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings while assuming a nonconcave production function. We prove that complex features exhibited are related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions.

scholarly journals The thalamic low-threshold Ca 2+ potential: a key determinant of the local and global dynamics of the slow (<1 Hz) sleep oscillation in thalamocortical networks

2011 ◽  
Vol 369 (1952) ◽  
pp. 3820-3839 ◽  
Author(s):  
Vincenzo Crunelli ◽  
Adam C. Errington ◽  
Stuart W. Hughes ◽  
Tibor I. Tóth
Keyword(s):  
Action Potential ◽  
Slow Oscillation ◽  
Global Dynamics ◽  
Action Potential Firing ◽  
Local And Global Dynamics ◽  
Up States ◽  
Potential Firing ◽  
Low Threshold

During non-rapid eye movement sleep and certain types of anaesthesia, neurons in the neocortex and thalamus exhibit a distinctive slow (<1 Hz) oscillation that consists of alternating UP and DOWN membrane potential states and which correlates with a pronounced slow (<1 Hz) rhythm in the electroencephalogram. While several studies have claimed that the slow oscillation is generated exclusively in neocortical networks and then transmitted to other brain areas, substantial evidence exists to suggest that the full expression of the slow oscillation in an intact thalamocortical (TC) network requires the balanced interaction of oscillator systems in both the neocortex and thalamus. Within such a scenario, we have previously argued that the powerful low-threshold Ca 2+ potential (LTCP)-mediated burst of action potentials that initiates the UP states in individual TC neurons may be a vital signal for instigating UP states in related cortical areas. To investigate these issues we constructed a computational model of the TC network which encompasses the important known aspects of the slow oscillation that have been garnered from earlier in vivo and in vitro experiments. Using this model we confirm that the overall expression of the slow oscillation is intricately reliant on intact connections between the thalamus and the cortex. In particular, we demonstrate that UP state-related LTCP-mediated bursts in TC neurons are proficient in triggering synchronous UP states in cortical networks, thereby bringing about a synchronous slow oscillation in the whole network. The importance of LTCP-mediated action potential bursts in the slow oscillation is also underlined by the observation that their associated dendritic Ca 2+ signals are the only ones that inform corticothalamic synapses of the TC neuron output, since they, but not those elicited by tonic action potential firing, reach the distal dendritic sites where these synapses are located.

COMPETITION AND COOPERATION ON PREDATION: BIFURCATION THEORY OF MUTUALISM

2021 ◽  
pp. 1-25
Author(s):  
SRIJANA GHIMIRE ◽  
XIANG-SHENG WANG
Keyword(s):  
Quantitative Information ◽  
Model Systems ◽  
Exclusion Principle ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Severe Condition ◽  
Predator Species ◽  
Competition And Cooperation ◽  
Local And Global Dynamics ◽  
Predator Prey Models

In this paper, we investigate two predator–prey models which take into consideration hunting cooperation (i.e., mutualism) between two different predators and within one predator species, respectively. Local and global dynamics are obtained for the model systems. By a detailed bifurcation analysis, we investigate the dependence of predation dynamics on mutualism (cooperative predation). From our study, we prove that mutualism may enhance the survival of mutualist predators in a severe condition and break the competitive exclusion principle. We further provide quantitative information about how the cooperative predation (mutualism) may (i) establish multiple stability switches on the positive equilibrium; (ii) generate backward bifurcation on equilibria; (iii) induce supercritical or subcritical Hopf bifurcations; and (iv) establish bi-stability phenomenon between the predator-free equilibrium and a positive equilibrium (or a limit cycle).

Equivalent Active Circuits of Distributed Control Systems

2000 ◽  
Author(s):  
H. S. Tzou ◽  
J. H. Ding
Keyword(s):  
Finite Difference ◽  
Distributed Parameter ◽  
Equivalent Circuits ◽  
Electronic Circuits ◽  
Research Issues ◽  
Modeling And Analysis ◽  
Finite Difference Equations ◽  
Dynamics And Control ◽  
Electric Signals ◽  
And Control

Abstract Modeling distributed parameter systems (DPS) by electronic circuits and fabricating the complicated equivalent circuits to evaluate the system characteristics always poses many challenging research issues for years. Modeling and analysis of distributed sensing/control of smart structures and distributed structronic systems are even scarce. This paper is to present a technique to model distributed structronic systems with electronic circuits and to evaluate control behaviors with the fabricated equivalent circuits. Electrical analogies and analysis of distributed structronic systems is proposed and dynamics and control of beam/sensor/actuator systems are investigated. To determine the equivalent circuits and system parameters, higher order partial derivatives are simplified using the finite difference method; partial differential equations (PDE) are transformed to finite difference equations and further represented by electronic components and circuits. To provide better signal management and stability, active electronic circuit systems are designed and fabricated. Electric signals from the distributed system circuits (i.e., soft and hard) are compared with results obtained by classical theoretical and other (e.g., the finite element, and experimental) techniques.

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