scholarly journals Global dynamics of a pine wilt disease transmission model with nonlinear incidence rates

2013 ◽  
Vol 37 (6) ◽  
pp. 4561-4569 ◽  
Author(s):  
Kwang Sung Lee ◽  
Daewook Kim
Keyword(s):  
Disease Transmission ◽  
Pine Wilt Disease ◽  
Incidence Rates ◽  
Wilt Disease ◽  
Transmission Model ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Pine Wilt ◽  
Nonlinear Incidence Rates ◽  
Disease Transmission Model

scholarly journals Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Ozair
Keyword(s):  
Global Analysis ◽  
Horizontal Transmission ◽  
Disease Model ◽  
Pine Wilt Disease ◽  
Incidence Rates ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Pine Wilt ◽  
Nonlinear Incidence Rates

The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable wheneverR0≤1. Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity.

scholarly journals Analysis of the Mathematical Model for the Spread of Pine Wilt Disease

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiangyun Shi ◽  
Guohua Song
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Endemic Equilibrium ◽  
Feasible Region ◽  
Global Dynamics ◽  
Pine Wilt ◽  
Theoretical Results ◽  
The Basic Reproduction Number

This paper formulates and analyzes a pine wilt disease model. Mathematical analyses of the model with regard to invariance of nonnegativity, boundedness of the solutions, existence of nonnegative equilibria, permanence, and global stability are presented. It is proved that the global dynamics are determined by the basic reproduction numberℛ0and the other valueℛcwhich is larger thanℛ0. Ifℛ0andℛcare both less than one, the disease-free equilibrium is asymptotically stable and the pine wilt disease always dies out. If one is between the two values, though the pine wilt disease could occur, the outbreak will stop. If the basic reproduction number is greater than one, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists. Numerical simulations are carried out to illustrate the theoretical results, and some disease control measures are especially presented by these theoretical results.

scholarly journals Pulse Roguing Strategy in a Pine Wilt Disease Epidemic Model with General Nonlinear Incidence Rate

2020 ◽  
Vol 08 (12) ◽  
pp. 2943-2953
Author(s):  
Quanben Sun ◽  
Wugui Chen ◽  
Zhicai Guo ◽  
Weiwei Ji ◽  
Jianping Wang
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Pine Wilt

scholarly journals Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates

2011 ◽  
Vol 39 (1-2) ◽  
pp. 15-34 ◽  
Author(s):  
Yoichi Enatsu ◽  
Eleonora Messina ◽  
Yukihiko Nakata ◽  
Yoshiaki Muroya ◽  
Elvira Russo ◽  
...  
Keyword(s):  
Wide Class ◽  
Epidemic Model ◽  
Incidence Rates ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Nonlinear Incidence Rates

scholarly journals Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ling Zhang ◽  
Jingmei Pang ◽  
Jinliang Wang
Keyword(s):  
Death Rate ◽  
Sufficient Conditions ◽  
Incidence Rates ◽  
Global Dynamics ◽  
Lyapunov Functionals ◽  
Natural Death ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates ◽  
Basic Production ◽  
Derivatives Of

We investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are obtained to ensure that the global dynamics are completely determined by the basic production numberR0. The proofs of the main results exploit the method of constructing Lyapunov functionals and a graph-theoretical technique in estimating the derivatives of Lyapunov functionals.

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