scholarly journals Lyapunov Function for a Dengue Transmission Model where two Species of Mosquitoes are Present: Global Stability

2017 ◽  
Vol 14 (10) ◽  
pp. 994-1004
Author(s):  
Puntani Pongsumpun ◽  
Rattiya Sungchasit ◽  
I Ming Tang
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Transmission Model ◽  
Dengue Transmission

scholarly journals Sensitivity, uncertainty and identifiability analyses to define a dengue transmission model with real data of an endemic municipality of Colombia

PLoS ONE ◽  
2020 ◽  
Vol 15 (3) ◽  
pp. e0229668
Author(s):  
Diana Paola Lizarralde-Bejarano ◽  
Daniel Rojas-Díaz ◽  
Sair Arboleda-Sánchez ◽  
María Eugenia Puerta-Yepes
Keyword(s):  
Real Data ◽  
Transmission Model ◽  
Dengue Transmission

scholarly journals Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model

2005 ◽  
Vol 2005 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

We first give sufficient conditions for the permanence of nonautonomous discrete ratio-dependent predator-prey model. By linearization of the model at positive solutions and construction of Lyapunov function, we also obtain some conditions which ensure that a positive solution of the model is stable and attracts all positive solutions.

scholarly journals Harvesting of a Single-Species System Incorporating Stage Structure and Toxicity

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Huiling Wu ◽  
Fengde Chen
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Optimal Policy ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Single Species ◽  
Structured Model ◽  
Bionomic Equilibrium ◽  
Maximal Principle

A single species stage-structured model incorporating both toxicant and harvesting is proposed and studied. It is shown that toxicant has no influence on the persistent property of the system. The existence of the bionomic equilibrium is also studied. After that, we consider the system with variable harvest effect; sufficient conditions are obtained for the global stability of bionomic equilibrium by constructing a suitable Lyapunov function. The optimal policy is also investigated by using Pontryagin's maximal principle. Some numeric simulations are carried out to illustrate the feasibility of the main results. We end this paper by a brief discussion.

scholarly journals Projections of increased and decreased dengue incidence under climate change

2016 ◽  
Vol 144 (14) ◽  
pp. 3091-3100 ◽  
Author(s):  
C. R. WILLIAMS ◽  
G. MINCHAM ◽  
H. FADDY ◽  
E. VIENNET ◽  
S. A. RITCHIE ◽  
...  
Keyword(s):  
Climate Change ◽  
Climate Warming ◽  
Carbon Emission ◽  
Climate Models ◽  
Virus Transmission ◽  
Transmission Model ◽  
Simple Relationship ◽  
Breeding Sites ◽  
Dengue Transmission ◽  
Dengue Epidemic

SUMMARYDengue is the world's most prevalent mosquito-borne disease, with more than 200 million people each year becoming infected. We used a mechanistic virus transmission model to determine whether climate warming would change dengue transmission in Australia. Using two climate models each with two carbon emission scenarios, we calculated future dengue epidemic potential for the period 2046–2064. Using the ECHAM5 model, decreased dengue transmission was predicted under the A2 carbon emission scenario, whereas some increases are likely under the B1 scenario. Dengue epidemic potential may decrease under climate warming due to mosquito breeding sites becoming drier and mosquito survivorship declining. These results contradict most previous studies that use correlative models to show increased dengue transmission under climate warming. Dengue epidemiology is determined by a complex interplay between climatic, human host, and pathogen factors. It is therefore naive to assume a simple relationship between climate and incidence, and incorrect to state that climate warming will uniformly increase dengue transmission, although in general the health impacts of climate change will be negative.

An SIR-Dengue transmission model with seasonal effects and impulsive control

2017 ◽  
Vol 289 ◽  
pp. 29-39 ◽  
Author(s):  
Joseph Páez Chávez ◽  
Thomas Götz ◽  
Stefan Siegmund ◽  
Karunia Putra Wijaya
Keyword(s):  
Impulsive Control ◽  
Seasonal Effects ◽  
Transmission Model ◽  
Dengue Transmission

A spatial echinococcosis transmission model with time delays: Stability and traveling waves

2017 ◽  
Vol 10 (06) ◽  
pp. 1750081 ◽  
Author(s):  
Zhiting Xu ◽  
Cuihua Ai
Keyword(s):  
Global Stability ◽  
Traveling Wave ◽  
Time Delays ◽  
Traveling Wave Solutions ◽  
Spatial Domain ◽  
Transmission Model ◽  
Initial Value ◽  
Wave Solutions ◽  
Number Formula ◽  
Disease Free

In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number [Formula: see text]. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder’s fixed point theorem and the limiting arguments, we show that when [Formula: see text], there exists a constant [Formula: see text] such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for [Formula: see text], and when [Formula: see text] and [Formula: see text], the model has no positive traveling wave solutions connecting them.

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