scholarly journals A mathematical analysis of the dynamics of chikungunya virus transmission

2021 ◽  
Vol 41 (1) ◽  
pp. 41-61
Author(s):  
Saiful Islam ◽  
Chandra Nath Podder
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Invariance Principle ◽  
Chikungunya Virus ◽  
Deterministic Model ◽  
Virus Transmission ◽  
Effective Prevention ◽  
Breeding Sites ◽  
Lasalle Invariance Principle ◽  
Effective Contact

In this paper, a deterministic model for the dynamics of chikungunya virus transmission is formulated and analyzed. It is shown that the model has a disease free equilibrium (DFE) and by using the basic reprodution number (R0) local stability of DFE is proved when  R0 < 1. Also, the global stability of DFE is investigated by Lyapunov function and LaSalle Invariance Principle. We show that there exists a unique endemic equilibrium (EE) of the model which is locally asymptotically stable whenever R0 > 1 and establish the global stability of the EE when R0 > 1, by using Lyapunov function and LaSalle Invariance Principle for a special case. Numerical simulations and sensitivity analysis show that the destruction of breeding sites and reduction of average life spans of vector would be effective prevention to control the outbreak. Controlling of effective contact rates and reducing transmissions probabilities may reduce the disease prevalence. GANITJ. Bangladesh Math. Soc.41.1 (2021) 41-61

The global stability of two epidemic models with nonlinear recovery incidence rate

2018 ◽  
Vol 32 (29) ◽  
pp. 1850357
Author(s):  
Yue Pan ◽  
Dechang Pi ◽  
Shuanglong Yao ◽  
Han Meng
Keyword(s):  
Lyapunov Function ◽  
Dynamic System ◽  
Global Stability ◽  
Incidence Rate ◽  
Invariance Principle ◽  
Epidemic Models ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
General Validity ◽  
Nonlinear Condition

In this paper, we present two epidemic models with a nonlinear incidence and transfer from infectious to recovery. For epidemic models, the basic reproductive number is calculated. A dynamic system based on threshold, using LaSalle’s invariance principle and Lyapunov function, is structured completely by the basic reproductive number. By studying the SIR and SIRS models under the nonlinear condition, the general validity of the method is verified.

GLOBAL STABILITY FOR A PHYTOPLANKTON-NUTRIENT SYSTEM

2000 ◽  
Vol 08 (02) ◽  
pp. 195-209 ◽  
Author(s):  
OLIVIER PARDO
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Global Stability ◽  
Invariance Principle ◽  
Global Asymptotic Stability ◽  
Lasalle’S Invariance Principle ◽  
Bacterial Decomposition ◽  
Autonomous Differential Equations ◽  
Lasalle's Invariance Principle

The model proposed by A. H. Taylor et al. [18] is discussed, with a view to determining the global asymptotic stability of the equilibria. The system consists of two autonomous differential equations, modeling the couple Phytoplankton-Nutrient with no delay on the recycling efficiency of nutrient by bacterial decomposition. Two distinct cases, persistence and extinction of phytoplankton are considered. In each case we will state the local and then the global stability of the equilibria by constructing an appropriate Lyapunov function and using the LaSalle's invariance principle. Also, in the case of extinction of phytoplankton we have introduced a supply of nutrient in the system and we have revealed the bloom of phytoplankton, which appears biologically in upwelling conditions.

scholarly journals Sequential Infection of Aedes aegypti Mosquitoes with Chikungunya Virus and Zika Virus Enhances Early Zika Virus Transmission

Insects ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 177 ◽  
Author(s):  
Tereza Magalhaes ◽  
Alexis Robison ◽  
Michael Young ◽  
William Black ◽  
Brian Foy ◽  
...  
Keyword(s):  
Aedes Aegypti ◽  
Blood Meal ◽  
Zika Virus ◽  
Chikungunya Virus ◽  
Vector Competence ◽  
Virus Transmission ◽  
Mosquito Vector ◽  
Molecular Aspects ◽  
Virus Interactions ◽  
Sequential Infection

In urban settings, chikungunya, Zika, and dengue viruses are transmitted by Aedes aegypti mosquitoes. Since these viruses co-circulate in several regions, coinfection in humans and vectors may occur, and human coinfections have been frequently reported. Yet, little is known about the molecular aspects of virus interactions within hosts and how they contribute to arbovirus transmission dynamics. We have previously shown that Aedes aegypti exposed to chikungunya and Zika viruses in the same blood meal can become coinfected and transmit both viruses simultaneously. However, mosquitoes may also become coinfected by multiple, sequential feeds on single infected hosts. Therefore, we tested whether sequential infection with chikungunya and Zika viruses impacts mosquito vector competence. We exposed Ae. aegypti mosquitoes first to one virus and 7 days later to the other virus and compared infection, dissemination, and transmission rates between sequentially and single infected groups. We found that coinfection rates were high after sequential exposure and that mosquitoes were able to co-transmit both viruses. Surprisingly, chikungunya virus coinfection enhanced Zika virus transmission 7 days after the second blood meal. Our data demonstrate heterologous arbovirus synergism within mosquitoes, by unknown mechanisms, leading to enhancement of transmission under certain conditions.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

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.

Risk of chikungunya virus transmission associated with European travelers returning from southern Thailand (2008–2015)

Transfusion ◽  
2019 ◽  
Vol 59 (8) ◽  
pp. 2612-2621 ◽  
Author(s):  
Hatsadee Appassakij ◽  
Paiwon Khuntikij ◽  
Khachornsakdi Silpapojakul ◽  
Charuporn Promwong ◽  
Pairaya Rujirojindakul ◽  
...  
Keyword(s):  
Chikungunya Virus ◽  
Virus Transmission ◽  
Southern Thailand

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.

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