Panic behavior induces multiple endemic states and backward bifurcation

2021 ◽  
Author(s):  
David Benítez ◽  
Ignacio Barradas
Keyword(s):  
Backward Bifurcation

scholarly journals Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model

2017 ◽  
Vol 12 (1) ◽  
pp. 51-88 ◽  
Author(s):  
Michael Barfield ◽  
Maia Martcheva ◽  
Necibe Tuncer ◽  
Robert D. Holt
Keyword(s):  
Backward Bifurcation ◽  
Epidemiological Model

scholarly journals Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

Vector Preference Annihilates Backward Bifurcation and Reduces Endemicity

2018 ◽  
Vol 81 (11) ◽  
pp. 4447-4469 ◽  
Author(s):  
Rocio Caja Rivera ◽  
Ignacio Barradas
Keyword(s):  
Backward Bifurcation

scholarly journals Modelling HIV dynamics with cell-to-cell transmission and CTL response

2021 ◽  
Author(s):  
Zirui Zhu ◽  
Ranchao Wu ◽  
Yu Yang ◽  
Yancong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Cell Interaction ◽  
Backward Bifurcation ◽  
Hiv Treatment ◽  
Hiv Model ◽  
Ctl Response ◽  
Hiv Dynamics ◽  
Subcritical Hopf Bifurcation ◽  
Cell Transmission ◽  
New Type

In most HIV models, the emergence of backward bifurcation means that the control for basic reproduction number less than one is no longer effective for HIV treatment. In this paper, we study an HIV model with CTL response and cell-to-cell transmission by using the dynamical approach. The local and global stability of equilibria is investigated, the relations of subcritical Hopf bifurcation and supercritical bifurcation points are revealed, especially, the so-called new type bifurcation is also found with two Hopf bifurcation curves meeting at the same Bogdanov-Takens bifurcation point. Forward and backward bifurcation, Hopf bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation are investigated analytically and numerically. Two limit cycles are also found numerically, which indicates that the complex behavior of HIV dynamics. Interestingly, the role of cell-to-cell interaction is fully uncovered, it may cause the oscillations to disappear and keep the so-called new type bifurcation persist. Finally, some conclusions and discussions are also given.

Exogenous re-infection does not always cause backward bifurcation in TB transmission dynamics

2017 ◽  
Vol 298 ◽  
pp. 322-335 ◽  
Author(s):  
Oluwaseun Y. Sharomi ◽  
Mohammad A. Safi ◽  
Abba B. Gumel ◽  
David J. Gerberry
Keyword(s):  
Backward Bifurcation ◽  
Transmission Dynamics

scholarly journals Backward Bifurcation and Optimal Control Analysis of a Trypanosoma brucei rhodesiense Model

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 971
Author(s):  
Mlyashimbi Helikumi ◽  
Moatlhodi Kgosimore ◽  
Dmitry Kuznetsov ◽  
Steady Mushayabasa
Keyword(s):  
Optimal Control ◽  
Trypanosoma Brucei ◽  
Backward Bifurcation ◽  
Effective Control ◽  
Control Analysis ◽  
Trypanosoma Brucei Rhodesiense ◽  
Awareness Campaigns ◽  
Human Animal ◽  
The Cost ◽  
Insecticide Control

In this paper, a mathematical model for the transmission dynamics of Trypanosoma brucei rhodesiense that incorporates three species—namely, human, animal and vector—is formulated and analyzed. Two controls representing awareness campaigns and insecticide use are investigated in order to minimize the number of infected hosts in the population and the cost of implementation. Qualitative analysis of the model showed that it exhibited backward bifurcation generated by awareness campaigns. From the optimal control analysis we observed that optimal awareness and insecticide use could lead to effective control of the disease even when they were implemented at low intensities. In addition, it was noted that insecticide control had a greater impact on minimizing the spread of the disease compared to awareness campaigns.

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