scholarly journals Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Oluwole Daniel Makinde ◽  
David Malonza
Keyword(s):  
Optimal Control ◽  
Typhoid Fever ◽  
Control Strategies ◽  
Cost Effective ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Effective Strategies ◽  
Next Generation Matrix ◽  
The Cost ◽  
Disease Free

We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.

scholarly journals TRANSMISSION DYNAMICS OF DENGUE IN COSTA RICA: THE ROLE OF HOSPITALIZATIONS

2019 ◽  
Vol 27 (1) ◽  
pp. 241-266
Author(s):  
FABIO SANCHEZ ◽  
JORGE ARROYO-ESQUIVEL ◽  
PAOLA VÁSQUEZ
Keyword(s):  
Costa Rica ◽  
Compartmental Model ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Specific Parameter ◽  
Public Health Officials ◽  
Disease Free

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals in the transmission dynamics of dengue in Costa Rica. The basic reproductive number, R0, is computed, as well as a sensitivity analysis on R0 parameters. The global stability of the disease-free equilibrium is established. Numerical simulations under specific parameter scenarios are performed to determine optimal prevention/control strategies.

scholarly journals Mathematical modelling for malaria under resistance and population movement

2020 ◽  
Vol 38 (2) ◽  
pp. 133-163
Author(s):  
Cristhian Montoya ◽  
Jhoana P. Romero Leiton
Keyword(s):  
Human Population ◽  
Control Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Transmission Dynamic ◽  
Equilibrium Solutions ◽  
Population Movements ◽  
Existence And Stability ◽  
Theoretical Results ◽  
Disease Free

In this work, two mathematical models for malaria under resistance are presented. More precisely, the first model shows the interaction between humans and mosquitoes inside a patch under infection of malaria when the human population is resistant to antimalarial drug and mosquitoes population is resistant to insecticides. For the second model, human–mosquitoes population movements in two patches is analyzed under the same malaria transmission dynamic established in a patch. For a single patch, existence and stability conditions for the equilibrium solutions in terms of the local basic reproductive number are developed. These results reveal the existence of a forward bifurcation and the global stability of disease–free equilibrium. In the case of two patches, a theoretical and numerical framework on sensitivity analysis of parameters is presented. After that, the use of antimalarial drugs and insecticides are incorporated as control strategies and an optimal control problem is formulated. Numerical experiments are carried out in both models to show the feasibility of our theoretical results.

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 Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Baba Seidu ◽  
Oluwole D. Makinde
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Nonlinear Dynamical System ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Nonlinear Dynamical ◽  
Basic Model ◽  
Hiv Aids

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number,R0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated whenR0<1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin’s Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.

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 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 Optimal Control and Cost Effectiveness Analysis of SIRS Malaria Disease Model with Temperature Variability Factor

2021 ◽  
Vol 53 (1) ◽  
pp. 134-163
Author(s):  
Temesgen Duressa Keno ◽  
Oluwole Daniel Makinde ◽  
Legesse Lemecha Obsu
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Initial Conditions ◽  
Control Strategies ◽  
Disease Model ◽  
Temperature Variability ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Bed Nets ◽  
Reproductive Number

In this study, we proposed and analyzed the optimal control and cost-effectiveness strategies for malaria epidemics model with impact of temperature variability. Temperature variability strongly determines the transmission of malaria. Firstly, we proved that all solutions of the model are positive and bounded within a certain set with initial conditions. Using the next-generation matrix method, the basic reproductive number at the present malaria-free equilibrium point was computed. The local stability and global stability of the malaria-free equilibrium were depicted applying the Jacobian matrix and Lyapunov function respectively when the basic reproductive number is smaller than one. However, the positive endemic equilibrium occurs when the basic reproductive number is greater than unity. A sensitivity analysis of the parameters was conducted; the model showed forward and backward bifurcation. Secondly, using Pontryagin’s maximum principle, optimal control interventions for malaria disease reduction are described involving three control measures, namely use of insecticide-treated bed nets, treatment of infected humans using anti-malarial drugs, and indoor residual insecticide spraying. An analysis of cost-effectiveness was also conducted. Finally, based on the simulation of different control strategies, the combination of treatment of infected humans and insecticide spraying was proved to be the most efficient and least costly strategy to eradicate the disease.

scholarly journals Mathematical Model on Optimal Combination of Vaccination and Antiviral Therapy to Curb In uenza in Kenya

2020 ◽  
pp. 134-147
Author(s):  
Derrick M. Nzioki ◽  
James K. Gatoto
Keyword(s):  
Numerical Simulations ◽  
Antiviral Therapy ◽  
Optimal Combination ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Human Influenza ◽  
Matlab Program ◽  
Next Generation Matrix ◽  
The Cost

Human influenza is a contagious disease which, if proper precautions are not taken to control the disease, can lead to massive mortality rates and high costs will be incurred to control the disease in case of an outbreak. As a result, we investigate how the cost of implementing both vaccination and antiviral therapy can be minimized and at the same time minimize the number of infected individuals. We have developed a system of ordinary differential equations from our formulated SVIR model and used vaccination and antiviral therapy to study influenza dynamics. We have the basic reproductive number determined using the next generation matrix. The equilibria and stability of the model has also been determined and analyzed. We have used the maximization theory of Pontryagin to define the optimal control rates and then used MATLAB program to do the numerical simulations. The numerical simulations done indicate that an ideal combination of vaccination and antiviral therapy decreases the number of infected individuals which in turn reduces the cost of applying the two control measures.

scholarly journals Optimal Control of Shigellosis with Cost-Effective Strategies

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Stephen Edward ◽  
Nyimvua Shaban ◽  
Eunice Mureithi
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Optimal Control Theory ◽  
Cost Effective ◽  
Incremental Cost Effectiveness Ratio ◽  
Cost Effectiveness Ratio ◽  
Effective Strategies ◽  
Education Campaign ◽  
Effectiveness Analysis ◽  
The Cost

In this paper, we apply optimal control theory to the model for shigellosis. It is assumed that education campaign, sanitation, and treatment are the main controls for this disease. The aim is to minimize the number of infections resulting from contact with careers, infectious population, and contaminated environments while keeping the cost of associated controls minimum. We achieve this aim through the application of Pontryagin’s Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth-order Runge-Kutta schemes. We simulate the model under different strategies to investigate which option could yield the best results. The findings show that the strategy combining all three control efforts (treatment, sanitation, and education campaign) proves to be more beneficial in containing shigellosis than the rest. On the other hand, cost-effectiveness analysis is performed via incremental cost-effectiveness ratio (ICER). The findings from the ICER show that a strategy incorporating all three controls (treatment, sanitation, and education campaign) is the most cost-effective of all strategies considered in the study.

scholarly journals Application and Optimal Control for an HBV Model with Vaccination and Treatment

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jing Zhang ◽  
Suxia Zhang
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Least Squares Method ◽  
Control Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Optimal Theory ◽  
B Virus ◽  
The Stability ◽  
Hbv Model

In this study, we formulate a model for hepatitis B virus with control strategies of newborn vaccination and treatment. Mathematical analysis is done theoretically and numerically. The results indicate that the stability of equilibria and persistence of the disease are determined by the basic reproductive number R0. Using the least squares method, the model is applied to simulate yearly new infected cases of hepatitis B in China from 2004 to 2016. Moreover, optimal control problem with newborn vaccination and treatment appearing as functions of time is analyzed by classical optimal theory. The existence of the solution to optimality system is proved, and the simulations are conducted to show the results when optimal control or current intervention is used.

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