scholarly journals Stability and Persistence of an Avian Influenza Epidemic Model with Impacts of Climate Change

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Xiao-Yan Zhao ◽  
Shu-Min Guo ◽  
Mini Ghosh ◽  
Xue-Zhi Li
Keyword(s):  
Climate Change ◽  
Seasonal Variation ◽  
Avian Influenza ◽  
Epidemic Model ◽  
Transmission Dynamics ◽  
Stability Conditions ◽  
Influenza Epidemic ◽  
Threshold Conditions ◽  
Disease Free ◽  
Impacts Of Climate Change

The growing number of reported avian influenza cases has prompted awareness of the importance of research methods to control the spread of the disease. Seasonal variation is one of the important factors that affect the spread of avian influenza. This paper presents a “nonautonomous” model to analyze the transmission dynamics of avian influenza with the effects of climate change. We obtain and discuss the global stability conditions of the disease-free equilibrium; the threshold conditions for persistence, permanence, and extinction of the disease; and the parameters with periodicity for controlling and eliminating the avian influenza.

scholarly journals An epidemic model for the transmission dynamics of HIV and another pathogen

2003 ◽  
Vol 45 (2) ◽  
pp. 181-193 ◽  
Author(s):  
S. M. Moghadas ◽  
A. B. Gumel
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Linear Model ◽  
Difference Method ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Transmission Dynamics ◽  
Optimal Therapy ◽  
Existence And Stability ◽  
Disease Free

AbstractA five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.

Modeling and scientific computing for the transmission dynamics of Avian influenza with half-saturated incidence

2020 ◽  
Vol 11 (04) ◽  
pp. 2050035
Author(s):  
Muhammad Altaf Khan ◽  
Saif Ullah ◽  
Yasir Khan ◽  
Muhammad Farhan
Keyword(s):  
Avian Influenza ◽  
Influenza Infection ◽  
Transmission Dynamics ◽  
Global Dynamics ◽  
Nonlinear Dynamical ◽  
Local And Global Dynamics ◽  
Proposed Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free

This paper presents the mathematical analysis of the dynamical system for avian influenza. The proposed model considers a nonlinear dynamical model of birds and human. The half-saturated incidence rate is used for the transmission of avian influenza infection. Rigorous mathematical results are presented for the proposed models. The local and global dynamics of each model are presented and proven that when [Formula: see text], then the disease-free equilibrium of each model is stable both locally and globally, and when [Formula: see text], then the endemic equilibrium is stable both locally and globally. The numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity.

STABILITY OF AN AGE-STRUCTURED SEIS EPIDEMIC MODEL WITH INFECTIVITY IN INCUBATIVE PERIOD

2010 ◽  
Vol 03 (03) ◽  
pp. 299-312 ◽  
Author(s):  
SHU-MIN GUO ◽  
XUE-ZHI LI ◽  
XIN-YU SONG
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Stability Conditions ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an age-structured SEIS epidemic model with infectivity in incubative period is formulated and studied. The explicit expression of the basic reproduction number R0 is obtained. It is shown that the disease-free equilibrium is globally asymptotically stable if R0 < 1, at least one endemic equilibrium exists if R0 > 1. The stability conditions of endemic equilibrium are also given.

scholarly journals Periodic synchronization of dengue epidemics in Thailand: the roles played by temperature and immunity

2021 ◽  
Author(s):  
Bernardo García-Carreras ◽  
Bingyi Yang ◽  
Mary K Grabowski ◽  
Lawrence W Sheppard ◽  
Angkana T Huang ◽  
...  
Keyword(s):  
Climate Change ◽  
Spatial Distribution ◽  
Seasonal Variation ◽  
Temporal Dynamics ◽  
Large Impact ◽  
Haemorrhagic Fever ◽  
Disease Patterns ◽  
Spatio Temporal ◽  
Dengue Epidemics ◽  
Impacts Of Climate Change

The spatial distribution of dengue and its vectors (spp. Aedes) may be the widest it has ever been, and projections suggest that climate change may allow the expansion to continue. However, the largest impacts of climate change on dengue might be in regions where the pathogen is already endemic. In these areas, the waxing and waning of immunity has a large impact on temporal dynamics of cases of dengue haemorrhagic fever. Here, we use 51 years of data across 72 provinces and characterise spatio-temporal patterns of dengue in Thailand, where dengue has caused almost 1.5 million cases over the last thirty years, and examine the roles played by temperature and dynamics of immunity in giving rise to those patterns. We find that timescales of multiannual oscillations in dengue vary in space and time and uncover an interesting spatial phenomenon: Thailand has experienced multiple, periodic synchronization events. We show that patterns in synchrony of dengue are consistent with those observed in temperature. Applying a temperature-driven dengue model, we explore how dynamics of immunity interact with temperature to produce the observed multiannual dynamics and patterns in synchrony. While multiannual oscillations are readily produced by immunity in absence of multiannual timescales in temperature, synchrony in temperature can synchronise dengue dynamics in different locations. However, at higher mean temperatures and lower seasonal variation, immune dynamics become more predominant, and dengue dynamics become more insensitive to multiannual fluctuations in temperature. These findings can help underpin predictions of disease patterns as global temperatures rise.

scholarly journals Dynamics for a stochastic delayed SIRS epidemic model

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Xiangyun Shi ◽  
Yimeng Cao ◽  
Xueyong Zhou
Keyword(s):  
Periodic Solution ◽  
Seasonal Variation ◽  
Global Existence ◽  
Positive Solutions ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sirs Epidemic Model ◽  
Nontrivial Periodic Solution ◽  
Well Posed ◽  
Disease Free

In this paper, we consider a stochastic delayed SIRS epidemic model with seasonal variation. Firstly, we prove that the system is mathematically and biologically well-posed by showing the global existence, positivity and stochastically ultimate boundneness of the solution. Secondly, some sufficient conditions on the permanence and extinction of the positive solutions with probability one are presented. Thirdly, we show that the solution of the system is asymptotical around of the disease-free periodic solution and the intensity of the oscillation depends of the intensity of the noise. Lastly, the existence of stochastic nontrivial periodic solution for the system is obtained.

STUDY OF A CARRIER DEPENDENT INFECTIOUS DISEASE — CHOLERA

2005 ◽  
Vol 13 (03) ◽  
pp. 233-244 ◽  
Author(s):  
PRASENJIT DAS ◽  
DEBASIS MUKHERJEE ◽  
A. K. SARKAR
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Epidemic Model ◽  
Free Carrier ◽  
Endemic Equilibrium ◽  
Stability Criteria ◽  
Threshold Conditions ◽  
Carrier Free ◽  
Existence Criteria ◽  
Disease Free

This paper analyzes an epidemic model for carrier dependent infectious disease — cholera. Existence criteria of carrier-free equilibrium point and endemic equilibrium point (unique or multiple) are discussed. Some threshold conditions are derived for which disease-free, carrier-free as well as endemic equilibrium become locally stable. Further global stability criteria of the carrier-free equilibrium and endemic equilibrium are achieved. Conditions for survival of all populations are also determined. Lastly numerical simulations are performed to validate the results obtained.

Analytical Solutions for an Avian Influenza Epidemic Model incorporating Spatial Spread as a Diffusive Process

2015 ◽  
Vol 5 (2) ◽  
pp. 150-159 ◽  
Author(s):  
Phontita Thiuthad ◽  
Valipuram S. Manoranjan ◽  
Yongwimon Lenbury
Keyword(s):  
Avian Influenza ◽  
Analytical Solutions ◽  
Epidemic Model ◽  
Travelling Wave ◽  
Phase Plane Analysis ◽  
Influenza Epidemic ◽  
Spatial Spread ◽  
Diffusive Process ◽  
Plane Analysis ◽  
Spatial Transmission

AbstractWe consider a theoretical model for the spread of avian influenza in a poultry population. An avian influenza epidemic model incorporating spatial spread as a diffusive process is discussed, where the infected individuals are restricted from moving to prevent spatial transmission but infection occurs when susceptible individuals come into contact with infected individuals or the virus is contracted from the contaminated environment (e.g. through water or food). The infection is assumed to spread radially and isotropically. After a stability and phase plane analysis of the equivalent system of ordinary differential equations, it is shown that an analytical solution can be obtained in the form of a travelling wave. We outline the methodology for finding such analytical solutions using a travelling wave coordinate when the wave is assumed to move at constant speed. Numerical simulations also produce the travelling wave solution, and a comparison is made with some predictions based on empirical data reported in the literature.

Sign in / Sign up

Export Citation Format

Share Document