Global dynamics of a Vector-Borne disease model with two delays and nonlinear transmission rate

2017 ◽  
Vol 40 (18) ◽  
pp. 6411-6423 ◽  
Author(s):  
Dan Tian ◽  
Haitao Song
Keyword(s):  
Transmission Rate ◽  
Disease Model ◽  
Global Dynamics ◽  
Nonlinear Transmission ◽  
Vector Borne Disease ◽  
Two Delays ◽  
Vector Borne

scholarly journals Global Dynamics of a Vector-Borne Disease Model with Two Transmission Routes

2020 ◽  
Vol 30 (06) ◽  
pp. 2050083
Author(s):  
Sk Shahid Nadim ◽  
Indrajit Ghosh ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Transmission Coefficient ◽  
Disease Model ◽  
Psychological Effect ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Direct Transmission ◽  
Vector Borne Disease ◽  
Indirect Transmission ◽  
Vector Borne

In this paper, we study the dynamics of a vector-borne disease model with two transmission paths: direct transmission through contact and indirect transmission through vector. The direct transmission is considered to be a nonmonotone incidence function to describe the psychological effect of some severe diseases among the population when the number of infected hosts is large and/or the disease possesses high case fatality rate. The system has a disease-free equilibrium which is locally asymptotically stable when the basic reproduction number ([Formula: see text]) is less than unity and may have up to four endemic equilibria. Analytical expression representing the epidemic growth rate is obtained for the system. Sensitivity of the two transmission pathways were compared with respect to the epidemic growth rate. We numerically find that the direct transmission coefficient is more sensitive than the indirect transmission coefficient with respect to [Formula: see text] and the epidemic growth rate. Local stability of endemic equilibrium is studied. Further, the global asymptotic stability of the endemic equilibrium is proved using Li and Muldowney geometric approach. The explicit condition for which the system undergoes backward bifurcation is obtained. The basic model also exhibits the hysteresis phenomenon which implies diseases will persist even when [Formula: see text] although the system undergoes a forward bifurcation and this phenomenon is rarely observed in disease models. Consequently, our analysis suggests that the diseases with multiple transmission routes exhibit bistable dynamics. However, efficient application of temporary control in bistable regions will curb the disease to lower endemicity. Additionally, numerical simulations reveal that the equilibrium level of infected hosts decreases as psychological effect increases.

scholarly journals Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease Model with Two Delays and Reinfection

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Yanxia Zhang ◽  
Long Li ◽  
Junjian Huang ◽  
Yanjun Liu
Keyword(s):  
Hopf Bifurcation ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Partial Protection ◽  
Center Manifold Theorem ◽  
Vector Borne Disease ◽  
Two Delays ◽  
Normal Form Method ◽  
Vector Borne ◽  
Delay Differential

In this paper, a vector-borne disease model with two delays and reinfection is established and considered. First of all, the existence of the equilibrium of the system, under different cases of two delays, is discussed through analyzing the corresponding characteristic equation of the linear system. Some conditions that the system undergoes Hopf bifurcation at the endemic equilibrium are obtained. Furthermore, by employing the normal form method and the center manifold theorem for delay differential equations, some explicit formulas used to describe the properties of bifurcating periodic solutions are derived. Finally, the numerical examples and simulations are presented to verify our theoretical conclusions. Meanwhile, the influences of the degree of partial protection for recovered people acquired by a primary infection on the endemic equilibrium and the critical values of the two delays are analyzed.

scholarly journals Global dynamics of a general vector-borne disease model with two transmission routes

2018 ◽  
Author(s):  
Sk Shahid Nadim ◽  
Indrajit Ghosh ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Transmission Coefficient ◽  
Disease Model ◽  
Case Fatality ◽  
Hysteresis Phenomenon ◽  
Global Dynamics ◽  
Direct Transmission ◽  
Vector Borne Disease ◽  
Indirect Transmission ◽  
Vector Borne

In this paper, we study the dynamics of a vector-borne disease model with two transmission paths: direct transmission through contact and indirect transmission through vector. The direct transmission is considered to be a non-monotone incidence function to describe the psychological effect of some severe diseases among the population when the number of infected hosts is large and/or the disease possesses high case fatality rate. The system has a disease-free equilibrium which is locally asymptomatically stable when the basic reproduction number (R_0) is less than unity and may have up to four endemic equilibria. Analytical expression representing the epidemic growth rate is obtained for the system. Sensitivity of the two transmission pathways were compared with respect to the epidemic growth rate. We numerically find that the direct transmission coefficient is more sensitive than the indirect transmission coefficient with respect to R_0 and the epidemic growth rate. Local stability of endemic equilibria is studied. Further, the global asymptotic stability of the endemic equilibrium is proved using Li and Muldowney geometric approach. The explicit condition for which the system undergoes backward bifurcation is obtained. The basic model also exhibits the hysteresis phenomenon which implies diseases will persist even when R_0<1 although the system undergoes a forward bifurcation and this phenomenon is rarely observed in disease models. Consequently, our analysis suggests that the diseases with multiple transmission routes exhibit bi-stable dynamics. However, efficient application of temporary control in bi-stable regions will curb the disease to lower endemicity. In addition, increase in transmission heterogeneity will increase the chance of disease eradication.

scholarly journals Stability, Bifurcation and Chaos Analysis of Vector-Borne Disease Model with Application to Rift Valley Fever

PLoS ONE ◽  
2014 ◽  
Vol 9 (10) ◽  
pp. e108172 ◽  
Author(s):  
Sansao A. Pedro ◽  
Shirley Abelman ◽  
Frank T. Ndjomatchoua ◽  
Rosemary Sang ◽  
Henri E. Z. Tonnang
Keyword(s):  
Rift Valley ◽  
Rift Valley Fever ◽  
Disease Model ◽  
Bifurcation And Chaos ◽  
Valley Fever ◽  
Chaos Analysis ◽  
Vector Borne Disease ◽  
Vector Borne

scholarly journals Qualitative behavior of vector-borne disease model

2016 ◽  
Vol 09 (03) ◽  
pp. 1382-1395
Author(s):  
Muhammad Ozair ◽  
Qamar Din ◽  
Takasar Hussain ◽  
Aziz Ullah Awan
Keyword(s):  
Disease Model ◽  
Qualitative Behavior ◽  
Vector Borne Disease ◽  
Vector Borne

scholarly journals Stability and Hopf Bifurcation of a Vector-Borne Disease Model with Saturated Infection Rate and Reinfection

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zhixing Hu ◽  
Shanshan Yin ◽  
Hui Wang
Keyword(s):  
Hopf Bifurcation ◽  
Infection Rate ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Cure Rate ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Stability

This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number R0, we determined the disease-free equilibrium E0 and the endemic equilibrium E1. Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium E1 by delay was studied, the existence of Hopf bifurcations of this system in E1 was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.

Analysis of a vector-borne disease model with impulsive perturbation and reinfection

2019 ◽  
Vol 5 (2) ◽  
pp. 359-381
Author(s):  
Suxia Zhang ◽  
Hongsen Dong ◽  
Xiaxia Xu ◽  
Xiaoqin Shen
Keyword(s):  
Disease Model ◽  
Vector Borne Disease ◽  
Vector Borne
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