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.

scholarly journals Dynamical and optimal control analysis of a seasonal Trypanosoma brucei rhodesiense model

2020 ◽  
Vol 17 (3) ◽  
pp. 2530-2556
Author(s):  
Mlyashimbi Helikumi ◽  
◽  
Moatlhodi Kgosimore ◽  
Dmitry Kuznetsov ◽  
Steady Mushayabasa ◽  
...  
Keyword(s):  
Optimal Control ◽  
Trypanosoma Brucei ◽  
Control Analysis ◽  
Trypanosoma Brucei Rhodesiense

A multi-delay model for pest control with awareness induced interventions — Hopf bifurcation and optimal control analysis

2020 ◽  
Vol 13 (06) ◽  
pp. 2050047
Author(s):  
Fahad Al Basir
Keyword(s):  
Optimal Control ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Time Delays ◽  
Control Strategies ◽  
Control Analysis ◽  
Agricultural Practice ◽  
Delay Model ◽  
Awareness Campaigns ◽  
Farming Awareness

Farming awareness is an important measure for pest controlling in agricultural practice. Time delay in controlling pest may affect the system. Time delay occurs in organizing awareness campaigns, also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media. Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays. Stability changes occur through Hopf-bifurcation when time delays cross the critical values. Optimal control theory has been applied for cost-effectiveness of the delayed system. Numerical simulations are carried out to justify the analytical results. This study shows that optimal farming awareness through radio, TV etc. can control the delay induced bifurcation in a cost-effective way.

scholarly journals Optimal Control and Cost-effectiveness Analysis of an HPV-Chlamydia Trachomatis co-infection model

2020 ◽  
Author(s):  
Andrew Omame ◽  
Celestine Uchenna Nnanna ◽  
Simeon Chioma Inyama
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Chlamydia Trachomatis ◽  
Reproduction Number ◽  
Population Level ◽  
Backward Bifurcation ◽  
Infection Model ◽  
Control Analysis ◽  
Number Of Individuals ◽  
Positive Population

In this work, a co-infection model for human papillomavirus (HPV) and Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease-free equilibrium of the co-infection model is \textbf{shown not to} be globally asymptotically stable, when the associated reproduction number is less unity. It is proven that the model undergoes the phenomenon of backward bifurcation when the associated reproduction number is less than unity. It is also shown that HPV re-infection ($\varepsilon\sst{p} \neq 0$) induced the phenomenon of backward bifurcation. Numerical simulations of the optimal control model showed that: (i) focusing on HPV intervention strategy alone (HPV prevention and screening), in the absence of Chlamydia trachomatis control, leads to a positive population level impact on the total number of individuals singly infected with Chlamydia trachomatis, (ii) Concentrating on Chlamydia trachomatis intervention controls alone (Chlamydia trachomatis prevention and treatment), in the absence of HPV intervention strategies, a positive population level impact is observed on the total number of individuals singly infected with HPV. Moreover, the strategy that combines and implements HPV and Chlamydia trachomatis prevention controls is the most cost-effective of all the control strategies in combating the co-infections of HPV and Chlamydia trachomatis.

scholarly journals Multiple Control Strategies for Prevention of Avian Influenza Pandemic

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Roman Ullah ◽  
Gul Zaman ◽  
Saeed Islam
Keyword(s):  
Optimal Control ◽  
Avian Influenza ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Effective Control ◽  
Multiple Control ◽  
Control Functions ◽  
The Cost

We present the prevention of avian influenza pandemic by adjusting multiple control functions in the human-to-human transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and numerical techniques, we investigate the cost-effective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method.

scholarly journals Zoonotic MERS-CoV transmission: modeling, backward bifurcation and optimal control analysis

2021 ◽  
Vol 103 (3) ◽  
pp. 2973-2992
Author(s):  
Indrajit Ghosh ◽  
Sk Shahid Nadim ◽  
Joydev Chattopadhyay
Keyword(s):  
Optimal Control ◽  
Backward Bifurcation ◽  
Control Analysis ◽  
Transmission Modeling

Optimal Control Problem of Vacination for The Spread of Measles Diseases Model

2018 ◽  
Vol 2 (2) ◽  
pp. 76
Author(s):  
Dani Suandi
Keyword(s):  
Optimal Control ◽  
Mortality Rate ◽  
Equation System ◽  
Vaccination Program ◽  
Control Analysis ◽  
Differential Equation System ◽  
Third Order ◽  
Vaccination Programs ◽  
The Cost ◽  
Very High

Measles is a disease in humans that is very contagious. Before the vaccine was known, the incidence of measles was very high, even the measles mortality rate reached 2.6 million every year. With the introduction of vaccines, the mortality rate in 2000-2016 can be reduced to 20.4 million deaths. Therefore, vaccination programs are very useful in reducing the incidence of measles. Unfortunately, we cannot know the optimal conditions for administering vaccines. The study of optimal control analysis of vaccination is needed in optimizing the prevention of the spread of measles. In this paper, a mathematical model which is a third-order differential equation system is constructed based on characteristic information on measles. The existence and locally stability of the equilibrium point are analyzed here. In addition, optimal control of the vaccination program also occurred. The results of our analysis suggest that the incidence of measles can decrease as the effectiveness of vaccination increases. But the effectiveness of vaccination is directly proportional to the costs incurred. If the cost incurred for the vaccination program more significant, the incidence of measles will decrease.

Alkaloid subfractions of Buxus sempervirens L. leaves with strong in vitro activity against Trypanosoma brucei rhodesiense

Planta Medica ◽  
2014 ◽  
Vol 80 (16) ◽  
Author(s):  
JB Althaus ◽  
G Jerz ◽  
P Winterhalter ◽  
M Kaiser ◽  
R Brun ◽  
...  
Keyword(s):  
Trypanosoma Brucei ◽  
Vitro Activity ◽  
In Vitro Activity ◽  
Trypanosoma Brucei Rhodesiense ◽  
Buxus Sempervirens

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

scholarly journals Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 929
Author(s):  
Guiyun Liu ◽  
Jieyong Chen ◽  
Zhongwei Liang ◽  
Zhimin Peng ◽  
Junqiang Li
Keyword(s):  
Optimal Control ◽  
Rapid Development ◽  
Hamiltonian Function ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Optimal Control Strategy ◽  
Epidemic Dynamics ◽  
Optimization Control ◽  
The Cost ◽  
The Pontryagin Maximum Principle

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

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