scholarly journals Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia

2020 ◽  
Author(s):  
Haileyesus Tessema Alemneh ◽  
Getachew Teshome Telahun
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Control Model ◽  
Control Analysis ◽  
Basic Model ◽  
Short Period ◽  
Disease Free

In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagins Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

scholarly journals Mathematical Analysis of a model for Chlamydia and Gonorrhea Codynamics with Optimal Control

2020 ◽  
Author(s):  
Eziaku Chinomso Chukukere ◽  
Simeon Chioma Inyama ◽  
Andrew Omame
Keyword(s):  
Optimal Control ◽  
Chlamydia Trachomatis ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Intervention Strategy ◽  
Infection Model ◽  
Control Analysis ◽  
Existence Of Optimal Control ◽  
The Impact ◽  
Disease Free

Abstract A model for Chlamydia trachomatis (CT) and Gonorrhea codynamics, with optimal control analysis is studied and analyzed to assess the impact of targetted treatment for each of the diseases on their co-infections in a population. The model exhibits the dynamical feature of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the co-infection model is also proven not to exist, when the associated reproduction number is below unity. The necessary conditions for the existence of optimal control and the optimality system for the co-infection model is established using the Pontryagin's Maximum Principle. Simulations of the optimal control model reveal that the intervention strategy which implements female Chlamydia trachomatis treatment and male gonorrhea treatment is the most effective in combating the co-infections of Chlamydia trachomatis and gonorrhea.

scholarly journals Optimal Control Analysis of Pneumonia and Meningitis Coinfection

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Getachew Teshome Tilahun
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Optimality System ◽  
Control Analysis ◽  
Prevention Effort ◽  
Treatment Effort ◽  
Basic Model

In this paper, we proposed a deterministic model of pneumonia-meningitis coinfection. We used a system of seven ordinary differential equations. Firstly, the qualitative behaviours of the model such as positivity of the solution, existence of the solution, the equilibrium points, basic reproduction number, analysis of equilibrium points, and sensitivity analysis are studied. The disease-free equilibrium is locally asymptotically stable if the basic reproduction number is kept less than unity, and conditions for global stability are established. Then, the basic model is extended to optimal control by incorporating four control interventions, such as prevention of pneumonia as well as meningitis and also treatment of pneumonia and meningitis diseases. The optimality system is obtained by using Pontryagin’s maximum principle. For simulation of the optimality system, we proposed five strategies to check the effect of the controls. First, we consider prevention only for both diseases, and the result shows that applying prevention control has a great impact in bringing down the expansion of pneumonia, meningitis, and their coinfection in the specified period of time. The other strategies are prevention effort for pneumonia and treatment effort for meningitis, prevention effort for meningitis and treatment effort for pneumonia, treatment effort for both diseases, and using all interventions. We obtained that each of the listed strategies is effective in minimizing the expansion of pneumonia-only, meningitis-only, and coinfectious population in the specified period of time.

scholarly journals The Dynamics and Optimal Control of a Hand-Foot-Mouth Disease Model

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Hongwu Tan ◽  
Hui Cao
Keyword(s):  
Optimal Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Disease Model ◽  
Mouth Disease ◽  
Infected People ◽  
Hand Foot Mouth Disease ◽  
The Cost ◽  
Existence Of Equilibria ◽  
Disease Free

We build and study the transmission dynamics of a hand-foot-mouth disease model with vaccination. The reproduction number is given, the existence of equilibria is obtained, and the global stability of disease-free equilibrium is proved by constructing the Lyapunov function. We also apply optimal control theory to the hand-foot-mouth disease model. The treatment and vaccination interventions are considered in the hand-foot-mouth disease model, and the optimal control strategies based on minimizing the cost of intervention and minimizing the number of the infected people are given. Numerical results show the usefulness of the optimization strategies.

scholarly journals A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

2020 ◽  
Author(s):  
Kenneth Uzoma Egeonu ◽  
Simeon Chioma Inyama ◽  
Andrew Omame
Keyword(s):  
Optimal Control ◽  
Drug Resistance ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Dynamical Property ◽  
Backward Bifurcation ◽  
Infection Model ◽  
Existence Of Optimal Control ◽  
The Impact ◽  
Disease Free

A mathematical model for two strains of Malaria and Cholera with optimal control is studied and analyzed to assess the impact of treatment controls in reducing the burden of the diseases in a population, in the presence of malaria drug resistance. The model is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is proven not to exist. The necessary conditions for the existence of optimal control and the optimality system for the model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.

scholarly journals A Co-infection model for HPV and Syphilis with Optimal Control and Cost-Effectiveness Analysis

2020 ◽  
Author(s):  
Andrew Omame ◽  
Daniel Okuonghae ◽  
Ugochukwu Emmanuel Nwafor ◽  
Benedict Udoka Odionyenma
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Control Strategies ◽  
Cost Effective ◽  
Infection Model ◽  
Control Analysis ◽  
Optimal Control Strategy ◽  
Disease Free

In this work, we develop and present a co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis. The full co-infection model is shown to undergo the phenomenon of backward bifurcation when a certain condition is satisfied. The global asymptotic stability of the disease-free equilibrium of the full model is shown \textbf{not to exist}, when the associated reproduction number is less than unity. The existence of endemic equilibrium of the syphilis-only sub-model is shown to exist and the global asymptotic stability of the disease-free and endemic equilibria of both the syphilis-only sub-model and HPV-only sub-model were established. The global asymptotic stability of disease-free equilibrium of the HPV-only sub-model is also proven. Numerical simulations of the optimal control model showed that the optimal control strategy which implements syphilis treatment controls for singly infected individuals is the most cost-effective of all the control strategies in reducing the burden of HPV and syphilis co-infections.

scholarly journals Transmission dynamics model of Tuberculosis with optimal control strategies in Haramaya district, Ethiopia

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Doyo Kereyu ◽  
Seleshi Demie
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Cost ◽  
Optimal Level ◽  
Qualitative Behavior ◽  
Dynamics Model ◽  
Haramaya District ◽  
Disease Free

AbstractIn this study, we use a compartmental nonlinear deterministic mathematical model to investigate the effect of different optimal control strategies in controlling Tuberculosis (TB) disease transmission in the community. We employ stability theory of differential equations to investigate the qualitative behavior of the model by obtaining the basic reproduction number and determining the local stability conditions for the disease-free and endemic equilibria. We consider three control strategies representing distancing, case finding, and treatment efforts and numerically compare the levels of exposed and infectious populations with and without control strategies. The results suggest that combination of all controls is the best strategy to eradicate TB disease from the community at an optimal level with minimum cost of interventions.

scholarly journals Optimal Control of Chlamydia Model with Vaccination

2020 ◽  
Author(s):  
Udoka Benedict Odionyenma ◽  
Dr. Andrew Omame ◽  
Nneka Onyinyechi Ukanwoke ◽  
Ikenna Nometa
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Infection Rate ◽  
Reproduction Number ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Threshold Value ◽  
Backward Bifurcation ◽  
Control Pair ◽  
Control Effort

This paper presents an SVEIRT epidemiological model in the human population with Chlamydia trachomatis. The model incorporated the vaccination class and investigated the role played by some control strategies in the dynamics of the disease (Chlamydia tracomatis). The reproduction number which helps in determining the rate of spread of the disease, was calculated using the method proosed by van den Driessche and Watmough. The local and global stability of the equilibrium points where established, where it was observed that the model is locally asymptotically stable if the reproduction number is less than unity, and globally stable if a certain threshold value is greater than unity or the re-infection rate is zero. The effect of the re-infection rate on the global stability suggests the exhibition of the phenomenon of backward bifurcation of the model. The backward bifurcation of the system was later studied, and it shows that backward bifurcation will occur if the value of the bifurcation parameter a is positive. The optimal control of the model shows the effect of different strategies in the transmission dynamicsof the disease and the cost effectivenes of each control pair. It was observed that the treatment and control effort gives the most cost effective combinations and at the same time the highest rate of disease avertion when compared to other stratagies. Sensitivity analysis of the parameters as shown in model, shows parameters that have high impact on the chosen classes.

scholarly journals Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amir Khan ◽  
Rahat Zarin ◽  
Usa Wannasingha Humphries ◽  
Ali Akgül ◽  
Anwar Saeed ◽  
...  
Keyword(s):  
Optimal Control ◽  
Existence And Uniqueness ◽  
Local Stability ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Control Analysis ◽  
Fractional Operator ◽  
Uniqueness Of The Solution ◽  
Alternative Type ◽  
Alternative Type Theorems

AbstractIn this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray–Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik–Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.

scholarly journals Modeling the Impact of Screening on the Transmission Dynamics of Human Papillomavirus with Optimal Control

2021 ◽  
Vol 16 ◽  
pp. 735-754
Author(s):  
Eshetu Dadi Gurmu ◽  
Boka Kumsa Bola ◽  
Purnachandra Rao Koya
Keyword(s):  
Optimal Control ◽  
Human Papillomavirus ◽  
Disease Transmission ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Screening Strategy ◽  
Existence And Stability ◽  
The Stability ◽  
The Impact ◽  
Disease Free

In this study, a nonlinear deterministic mathematical model of Human Papillomavirus was formulated. The model is studied qualitatively using the stability theory of differential equations. The model is analyzed qualitatively for validating the existence and stability of disease ¬free and endemic equilibrium points using a basic reproduction number that governs the disease transmission. It's observed that the model exhibits a backward bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies viz. prevention strategy, treatment strategy, and screening strategy. Numerical results of the optimal control model reveal that a combination of prevention, screening, and treatment is the most effective strategy to wipe out the disease in the community.

Optimal Control Analysis of a Cholera Epidemic Model

2019 ◽  
Vol 14 (01) ◽  
pp. 27-48 ◽  
Author(s):  
Prabir Panja
Keyword(s):  
Optimal Control ◽  
Vibrio Cholerae ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Human Population ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Control Analysis ◽  
Number Formula ◽  
The Basic Reproduction Number

In this paper, a cholera disease transmission mathematical model has been developed. According to the transmission mechanism of cholera disease, total human population has been classified into four subpopulations such as (i) Susceptible human, (ii) Exposed human, (iii) Infected human and (iv) Recovered human. Also, the total bacterial population has been classified into two subpopulations such as (i) Vibrio Cholerae that grows in the infected human intestine and (ii) Vibrio Cholerae in the environment. It is assumed that the cholera disease can be transmitted in a human population through the consumption of contaminated food and water by Vibrio Cholerae bacterium present in the environment. Also, it is assumed that Vibrio Cholerae bacterium is spread in the environment through the vomiting and feces of infected humans. Positivity and boundedness of solutions of our proposed system have been investigated. Equilibrium points and the basic reproduction number [Formula: see text] are evaluated. Local stability conditions of disease-free and endemic equilibrium points have been discussed. A sensitivity analysis has been carried out on the basic reproduction number [Formula: see text]. To eradicate cholera disease from the human population, an optimal control problem has been formulated and solved with the help of Pontryagin’s maximum principle. Here treatment, vaccination and awareness programs have been considered as control parameters to reduce the number of infected humans from cholera disease. Finally, the optimal control and the cost-effectiveness analysis of our proposed model have been performed numerically.

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