scholarly journals Mathematical Model for Malaria Transmission with Optimal Control Strategies and Their Effects

2018 ◽  
Vol 20 (3) ◽  
pp. 1-16
Author(s):  
Mojeeb AL-Rahman EL-Nor Osman ◽  
Appiagyei Ebenezer ◽  
Isack E. Kibona
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Malaria Transmission ◽  
Control Strategies

scholarly journals Control measures of malaria transmission in Rwanda based on SEIR SEI mathematical model

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Emmanuel Hakizimana ◽  
Jean Marie Ntaganda
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Malaria Transmission ◽  
Optimal Control Problems ◽  
Control Strategies ◽  
Control Measures ◽  
Bed Nets ◽  
Infected People ◽  
Insecticide Treated Bed Nets ◽  
Malaria Model

This research paper investigated the dynamics of malaria transmission in Rwanda using the nonlinear forces of infections which are included in SEIR-SEI mathematical model for human and mosquito populations. The mathematical modeling of malaria studies the interaction among the human and mosquito populations in controlling malaria transmission and eventually eliminating malaria infection. This work investigates the optimal control strategies for minimizing the rate of malaria transmission by applying three control variables through Caputo fractional derivative. The optimal control problems for malaria model found the control parameters which minimize infection. The numerical simulation showed that the number of exposed and infected people and mosquito population are decreased due to the control strategies. Finally, this work found out that the transmission of malaria in Rwanda can be minimized by using the combination of controls like Insecticide Treated bed Nets (ITNs), Indoor Residual Spray (IRS) and Artemisinin based Combination Therapies (ACTs).

scholarly journals Optimal Control Strategies in an Alcoholism Model

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Xun-Yang Wang ◽  
Hai-Feng Huo ◽  
Qing-Kai Kong ◽  
Wei-Xuan Shi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Control Strategies ◽  
Pontryagin’S Maximum Principle ◽  
Social Phenomenon ◽  
Pontryagin's Maximum Principle ◽  
Existence And Stability ◽  
Objective Functional

This paper presents a deterministic SATQ-type mathematical model (including susceptible, alcoholism, treating, and quitting compartments) for the spread of alcoholism with two control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, existence and stability are analyzed. The optimal control strategies are derived by proposing an objective functional and using Pontryagin’s Maximum Principle. Numerical simulations are also conducted in the analytic results.

scholarly journals Estimating the Optimal Control of Zoonotic Visceral Leishmaniasis by the Use of a Mathematical Model

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Laila Massad Ribas ◽  
Vera Lucia Zaher ◽  
Helio Junji Shimozako ◽  
Eduardo Massad
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Visceral Leishmaniasis ◽  
Vector Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Effective Control ◽  
Alternative Control ◽  
Alternative Strategies ◽  
Zoonotic Visceral Leishmaniasis

We argue that the strategy of culling infected dogs is not the most efficient way to control zoonotic visceral leishmaniasis (ZVL) and that, in the presence of alternative control strategies with better potential results, official programs of compulsory culling adopted by some countries are inefficient and unethical. We base our arguments on a mathematical model for the study of control strategies against ZVL, which allows the comparison of the efficacies of 5, alternative strategies. We demonstrate that the culling program, previously questioned on both theoretical and practical grounds is the less effective control strategy. In addition, we show that vector control and the use of insecticide-impregnated dog collars are, by far, more efficient at reducing the prevalence of ZVL in humans.

scholarly journals Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Jairos Kahuru ◽  
Livingstone S. Luboobi ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Control Process ◽  
Control Measures ◽  
Human Beings ◽  
Optimal Control Strategy ◽  
Control Techniques ◽  
Existence Of Optimal Control

Tungiasis is a permanent penetration of female sand flea“Tunga penetrans”into the epidermis of its host. It affects human beings and domestic and sylvatic animals. In this paper, we apply optimal control techniques to a Tungiasis controlled mathematical model to determine the optimal control strategy in order to minimize the number of infested humans, infested animals, and sand flea populations. In an attempt to reduce Tungiasis infestation in human population, the control strategies based on personal protection, personal treatment, educational campaign, environmental sanitation, and insecticidal treatments on the affected parts as well as on animal fur are considered. We prove the existence of optimal control problem, determine the necessary conditions for optimality, and then perform numerical simulations. The numerical results showed that the control strategy comprises all five control measures and that which involves the three control measures of insecticide control, insecticidal dusting on animal furs, and environmental hygiene has the significant impact on Tungiasis transmission. Therefore, fighting against Tungiasis infestation in endemic settings, multidimensional control process should be employed in order to achieve the maximum benefits.

scholarly journals Analysis of Control Interventions against Malaria in communities with Limited Resources

2021 ◽  
Vol 29 (2) ◽  
pp. 71-91
Author(s):  
E.A. Bakare ◽  
B.O. Onasanya ◽  
S. Hoskova-Mayerova ◽  
O. Olubosede
Keyword(s):  
Optimal Control ◽  
Malaria Transmission ◽  
Control Strategies ◽  
Indoor Residual Spraying ◽  
Control Measures ◽  
Limited Resources ◽  
Effective Control ◽  
Bed Nets ◽  
Multiple Control ◽  
Potential Impact

Abstract The aim of this paper is to analyse the potential impact of multiple current interventions in communities with limited resources in order to obtain optimal control strategies and provide a basis for future predictions of the most effective control measures against the spread of malaria. We developed a population-based model of malaria transmission dynamics to investigate the effectiveness of five different interventions. The model captured both the human and the mosquito compartments. The control interventions considered were: educational campaigns to mobilise people for diagnostic test and treatment and to sleep under bed nets; treatment through mass drug administration; indoor residual spraying(IRS) with insecticide to reduce malaria transmission; insecticide treated net (ITN) to reduce morbidity; and regular destruction of mosquito breeding sites to reduce the number of new mosquito and bites/contact at dusks and dawn. Analysis of the potential impact of the multiple control interventions were carried out and the optimal control strategies that minimized the number of infected human and mosquito and the cost of applying the various control interventions were determined.

scholarly journals Optimization of the Controls against the Spread of Zika Virus in Populations

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 76
Author(s):  
Gilberto González-Parra ◽  
Miguel Díaz-Rodríguez ◽  
Abraham J. Arenas
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Zika Virus ◽  
Control Strategies ◽  
Real Life ◽  
Real Data ◽  
Control Measures ◽  
Information Campaigns ◽  
Control Functions ◽  
Cost Efficient

In this paper, we study and explore two control strategies to decrease the spread of Zika virus in the human and mosquito populations. The control strategies that we consider in this study are awareness and spraying campaigns. We solve several optimal control problems relying on a mathematical epidemic model of Zika that considers both human and mosquito populations. The first control strategy is broad and includes using information campaigns, encouraging people to use bednetting, wear long-sleeve shirts, or similar protection actions. The second control is more specific and relies on spraying insecticides. The control system relies on a Zika mathematical model with control functions. To develop the optimal control problem, we use Pontryagins’ maximum principle, which is numerically solved as a boundary value problem. For the mathematical model of the Zika epidemic, we use parameter values extracted from real data from an outbreak in Colombia. We study the effect of the costs related to the controls and infected populations. These costs are important in real life since they can change the outcomes and recommendations for health authorities dramatically. Finally, we explore different options regarding which control measures are more cost-efficient for society.

scholarly journals The co-dynamics of Hepatitis E and HIV

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4723-4745
Author(s):  
Ebraheem Alzahrani ◽  
Muhammad Khan
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Bifurcation Analysis ◽  
Disease Burden ◽  
Control Strategies ◽  
Hepatitis E ◽  
Control Model ◽  
Full Model ◽  
Dynamics Model ◽  
Infection Dynamics

This work investigates the co-dynamics of Hepatitis E and HIV. Initially, we formulate a co-infection dynamics model of Hepatitis E and HIV. Then, we analyze each model and discuss their mathematical results. After that, we investigate the full model and present their basic mathematical results. A bifurcation analysis for full model is investigated. Further, we formulate a mathematical model with five controls. Optimal control model is formulated and the necessary results of the optimal control characterization are presented. Moreover, numerical results with different control strategies are presented. It is shown that each strategy has its own importance but for the disease elimination the combination of all the five controls at the same time can best decrease the disease burden from the community.

scholarly journals Optimizing systemic insecticide use to improve malaria control

2019 ◽  
Author(s):  
Hannah R. Meredith ◽  
Luis Furuya-Kanamori ◽  
Laith Yakob
Keyword(s):  
Mathematical Model ◽  
Malaria Transmission ◽  
Malaria Control ◽  
Mass Drug Administration ◽  
Mosquito Control ◽  
Pyrethroid Resistance ◽  
Control Strategies ◽  
Systemic Insecticide ◽  
Systemic Insecticides ◽  
Long Lasting Insecticidal Nets

AbstractLong lasting insecticidal nets and indoor residual sprays have significantly reduced the burden of malaria. However, several hurdles remain before elimination can be achieved: mosquito vectors have developed resistance to public health insecticides, including pyrethroids, and have altered their biting behaviour to avoid these indoor control tools. Systemic insecticides, drugs applied directly to blood-hosts to kill mosquitoes that take a blood meal, offer a promising vector control option. To date, most studies focus on repurposing ivermectin, a drug used extensively to treat river blindness. There is concern that over-dependence on a single drug will inevitably repeat past experiences with the rapid spread of pyrethroid resistance in malaria vectors. Diversifying the arsenal of systemic insecticides used for mass drug administration would improve this strategy’s sustainability. Here, a review was conducted to identify systemic insecticide candidates and consolidate their pharmacokinetic/pharmacodynamic properties. The impact of alternative integrated vector control options and different dosing regimens on malaria transmission reduction are illustrated through a mathematical model simulation. The review identified drugs from four classes commonly used in livestock and companion animals: avermectics, milbemycins, isoxazolines, and spinosyns. Simulations predicted that isoxazoline and spinosyn drugs were promising candidates for mass drug administration, as they were predicted to need less frequent application than avermectins and milbemycins to maintain mosquitocidal blood concentrations. These findings will provide a guide for investigating and applying different systemic insecticides to achieve better mosquito control strategies.SignificanceThe widespread use of long lasting insecticidal nets (LLINs) and indoor residual spray has selected for mosquitoes that are resistant to pyrethroids or avoid exposure by feeding outdoors or on livestock. Systemic insecticides, drugs that render a host’s blood toxic to feeding mosquitoes, could be an effective control strategy for mosquitoes with pyrethroid resistance and/or outdoor feeding tendencies. Here, a number of existing systemic insecticide candidates are identified and their pharmacokinetic properties in different drug-host-route scenarios consolidated. These data were used to parameterise a mathematical model that illustrated the projected gains achievable in malaria control programmes already employing LLINs. The findings provide a guide for investigating and applying different systemic insecticides to improve mosquito control strategies and reduce malaria transmission.

scholarly journals Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Kwang Sung Lee
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Pine Wilt ◽  
The Stability ◽  
The Basic Reproduction Number

We propose a mathematical model of pine wilt disease (PWD) which is caused by pine sawyer beetles carrying the pinewood nematode (PWN). We calculate the basic reproduction numberR0and investigate the stability of a disease-free and endemic equilibrium in a given mathematical model. We show that the stability of the equilibrium in the proposed model can be controlled through the basic reproduction numberR0. We then discuss effective optimal control strategies for the proposed PWD mathematical model. We demonstrate the existence of a control problem, and then we apply both analytical and numerical techniques to demonstrate effective control methods to prevent the transmission of the PWD. In order to do this, we apply two control strategies: tree-injection of nematicide and the eradication of adult beetles through aerial pesticide spraying. Optimal prevention strategies can be determined by solving the corresponding optimality system. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that reducing the number of pine sawyer beetles is more effective than the tree-injection strategy for controlling the spread of PWD.

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