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.

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.

A MODEL FOR VECTOR TRANSMITTED DISEASES WITH SATURATION INCIDENCE

2001 ◽  
Vol 09 (04) ◽  
pp. 235-245 ◽  
Author(s):  
LOURDES ESTEVA ◽  
MARIANO MATIAS
Keyword(s):  
Endemic Equilibrium ◽  
Saturation Effect ◽  
Basic Reproductive Number ◽  
Infected Host ◽  
Reproductive Number ◽  
The Stability ◽  
Stability Results ◽  
Disease Free

A model for a disease that is transmitted by vectors is formulated. All newborns are assumed susceptible, and human and vector populations are assumed to be constant. The model assumes a saturation effect in the incidences due to the response of the vector to change in the susceptible and infected host densities. Stability of the disease free equilibrium and existence, uniqueness and stability of the endemic equilibrium is investigated. The stability results are given in terms of the basic reproductive number R0.

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.

Impact of climate factors on contact rate of vector-borne diseases: Case study of malaria

2016 ◽  
Vol 10 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Ezekiel Dangbé ◽  
Antoine Perasso ◽  
Damakoa Irépran ◽  
David Békollé
Keyword(s):  
Environmental Changes ◽  
Temporal Distribution ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Contact Rate ◽  
Vector Borne Diseases ◽  
Transmission Period ◽  
Vector Borne ◽  
The Stability ◽  
The Impact

Climate change influences more and more of our activities. These changes led to environmental changes which has in turn affected the spatial and temporal distribution of the incidence of vector-borne diseases. To establish the impact of climate on contact rate of vector-borne diseases, we examine the variation of prevalence of diseases according to season. In this paper, the goal is to establish that the basic reproductive number [Formula: see text] depends on the duration of transmission period and the date of the first conta-mination case that was declared ([Formula: see text]) in the specific case of malaria. We described the dynamics of transmission of malaria by using non-autonomous differential equations. We analyzed the stability of endemic equilibrium (EE) and disease-free equilibrium (DFE). We prove that the persistence of disease depends on minimum and maximum values of contact rate of vector-borne diseases.

scholarly journals Huanglongbing Model under the Control Strategy of Discontinuous Removal of Infected Trees

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1164
Author(s):  
Weiwei Ling ◽  
Pinxia Wu ◽  
Xiumei Li ◽  
Liangjin Xie
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Control Strategy ◽  
Theoretical Basis ◽  
Dynamic Properties ◽  
Transmission Mechanism ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Vector Borne ◽  
Citrus Trees

By using differential equations with discontinuous right-hand sides, a dynamic model for vector-borne infectious disease under the discontinuous removal of infected trees was established after understanding the transmission mechanism of Huanglongbing (HLB) disease in citrus trees. Through calculation, the basic reproductive number of the model can be attained and the properties of the model are discussed. On this basis, the existence and global stability of the calculated equilibria are verified. Moreover, it was found that different I0 in the control strategy cannot change the dynamic properties of HLB disease. However, the lower the value of I0, the fewer HLB-infected citrus trees, which provides a theoretical basis for controlling HLB disease and reducing expenditure.

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 Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

2020 ◽  
pp. 8-19
Author(s):  
Laid Chahrazed
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability ◽  
Disease Free ◽  
Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

scholarly journals Understanding the effect of temperature on Bluetongue disease risk in livestock

2019 ◽  
Author(s):  
Fadoua El Moustaid ◽  
Zorian Thronton ◽  
Hani Slamani ◽  
Sadie J. Ryan ◽  
Leah R. Johnson
Keyword(s):  
Disease Risk ◽  
Vector Competence ◽  
Basic Reproductive Number ◽  
Effect Of Temperature ◽  
Reproductive Number ◽  
Temperature Sensitive ◽  
Modeling Tools ◽  
Vector Borne Diseases ◽  
Thermal Range ◽  
Vector Borne

AbstractThe transmission of vector-borne diseases is governed by complex factors including pathogen characteristics, vector-host interactions, and environmental conditions. Temperature is a major driver for many vector-borne diseases including Bluetongue viral (BTV) disease, a midge-borne febrile disease of ruminants, notably livestock, whose etiology ranges from mild or asymptomatic to rapidly fatal, thus threatening animal agriculture and the economy of affected countries. Using modeling tools, we seek to predict where transmission can occur based on suitable temperatures for BTV. We fit thermal performance curves to temperature sensitive midge life history traits, using a Bayesian approach. Then, we incorporated these into a new formula for the disease basic reproductive number, R0, to include trait responses, for two species of key midge vectors, Culicoides sonorensis and Culicoides variipennis. Our results show that outbreaks of BTV are more likely between 15°C and 33°C with predicted peak transmission at 26°C. The greatest uncertainty in R0 is associated with the uncertainty in: mortality and fecundity of midges near optimal temperature for transmission; midges’ probability of becoming infectious post infection at the lower edge of the thermal range; and the biting rate together with vector competence at the higher edge of the thermal range. We compare our R0 to two other R0 formulations and show that incorporating thermal curves into all three leads to similar BTV risk predictions. To demonstrate the utility of this model approach, we created global suitability maps indicating the areas at high and long-term risk of BTV transmission, to assess risk, and anticipate potential locations of establishment.

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