scholarly journals Modelling Optimal Control of In-Host HIV Dynamics Using Different Control Strategies

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Purity Ngina ◽  
Rachel Waema Mbogo ◽  
Livingstone S. Luboobi
Keyword(s):  
Optimal Control ◽  
Deterministic Model ◽  
Control Strategies ◽  
Treatment Strategies ◽  
Optimal Strategies ◽  
Hiv Treatment ◽  
Sub Saharan Africa ◽  
System Control ◽  
Hiv Dynamics

HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles played by the various HIV treatment strategies. In particular, we establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables. We have applied Pontryagin’s Maximum Principle in characterizing the optimality control, which then has been solved numerically by applying the Runge-Kutta forth-order scheme. The numerical results indicate that an optimal controlled treatment strategy would ensure significant reduction in viral load and also in HIV transmission. It is also evident from the results that protease inhibitor plays a key role in virus suppression; this is not to underscore the benefits accrued when all the three drug regimes are used in combination.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

scholarly journals Optimal control of acute myeloid leukaemia

2018 ◽  
Author(s):  
Jesse A Sharp ◽  
Alexander P Browning ◽  
Tarunendu Mapder ◽  
Kevin Burrage ◽  
Matthew J Simpson
Keyword(s):  
Optimal Control ◽  
Immune Response ◽  
Acute Myeloid Leukaemia ◽  
Myeloid Leukaemia ◽  
Cell Model ◽  
Control Strategies ◽  
Treatment Strategies ◽  
Numerical Convergence ◽  
Stem Cell Model ◽  
Acute Myeloid

AbstractAcute myeloid leukaemia (AML) is a blood cancer affecting haematopoietic stem cells. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagin’s Maximum Principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available.

Dynamical analysis of a class of hepatitis C virus infection models with application of optimal control

2016 ◽  
Vol 09 (03) ◽  
pp. 1650038 ◽  
Author(s):  
Aida Mojaver ◽  
Hossein Kheiri
Keyword(s):  
Optimal Control ◽  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Deterministic Model ◽  
Treatment Strategies ◽  
Dynamical Analysis ◽  
Existence And Stability ◽  
Direct Cell ◽  
Infected Cells ◽  
The Impact

In this paper, we deal with the problem of optimal control of a deterministic model of hepatitis C virus (HCV). In the first part of our analysis, a mathematical modeling of HCV dynamics which can be controlled by antiretroviral therapy as fixed controls has been presented and analyzed which incorporates two mechanisms: infection by free virions and the direct cell-to-cell transmission. Basic reproduction number is calculated and the existence and stability of equilibria are investigated. In the second part, the optimal control problem representing drug treatment strategies of the model is explored considering control parameters as time-dependent in order to minimize not only the population of infected cells but also the associated costs. At the end of the paper, the impact of combination of the strategies in the control of HCV and their effectiveness are compared by numerical simulation.

Estimating the impact of antiretroviral therapy on HIV-TB co-infection: Optimal strategy prediction

2020 ◽  
pp. 2150004
Author(s):  
Tanvi ◽  
Rajiv Aggarwal
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Treatment Strategies ◽  
Hiv Treatment ◽  
Time Dependent ◽  
Control Parameters ◽  
Treatment Rate ◽  
Tb Treatment ◽  
The Cost ◽  
The Impact

In this paper, a nonlinear population model for HIV-TB co-infection has been proposed. The model is incorporated with the effect of early and late initiation of HIV treatment in co-infectives already on TB treatment, on the occurrence of Immune Reconstitution Inflammatory syndrome (IRIS). A 15-dimensional (15D) mathematical model has been developed in this study. We begin with considering constant treatment rates and thereafter, proceed to time-dependent treatment rates for co-infectives as control parameters. The basic reproduction number, a threshold quantity, corresponding to each HIV and TB sub-model has been computed in case of constant controls. With constant values of control parameters, mathematical analysis shows the existence and local stability of the disease-free equilibrium point and the endemic equilibrium point for the model. Together with time-dependent parameters, an optimal control problem is introduced and solved using Pontryagin’s maximum principle with an objective to minimize the number of infectives and disease induced deaths along with the cost of treatment. Numerical simulations are performed to examine the effect of reproduction numbers on control profiles and to identify, the ideal combination of treatment strategies which provides minimum burden on a society. Numerical results imply that if both HIV and TB are endemic in the population, then in order to bring in minimum burden from the co-infection, optimal control efforts must be enforced rather than constant treatment rate.

scholarly journals Application of Optimal Control to Influenza Pneumonia Coinfection with Antiviral Resistance

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Caroline W. Kanyiri ◽  
Livingstone Luboobi ◽  
Mark Kimathi
Keyword(s):  
Optimal Control ◽  
Optimal Strategies ◽  
Antiviral Resistance ◽  
System Control ◽  
High Morbidity ◽  
Prevention Measures ◽  
Sweep Method ◽  
Influenza Pneumonia ◽  
Major Impediment ◽  
Forward Backward Sweep Method

Influenza and pneumonia independently lead to high morbidity and mortality annually among the human population globally; however, a glaring fact is that influenza pneumonia coinfection is more vicious and it is a threat to public health. Emergence of antiviral resistance is a major impediment in the control of the coinfection. In this paper, a deterministic mathematical model illustrating the transmission dynamics of influenza pneumonia coinfection is formulated having incorporated antiviral resistance. Optimal control theory is then applied to investigate optimal strategies for controlling the coinfection using prevalence reduction and treatment as the system control variables. Pontryagin’s maximum principle is used to characterize the optimal control. The derived optimality system is solved numerically using the Runge–Kutta-based forward-backward sweep method. Simulation results reveal that implementation of prevention measures is sufficient to eradicate influenza pneumonia coinfection from a given population. The prevention measures could be social distancing, vaccination, curbing mutation and reassortment, and curbing interspecies movement of the influenza virus.

scholarly journals Transmission Dynamics of Hepatitis C with Control Strategies

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Adnan Khan ◽  
Sultan Sial ◽  
Mudassar Imran
Keyword(s):  
Optimal Control ◽  
Hepatitis C ◽  
Deterministic Model ◽  
Control Strategies ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Critical Parameters ◽  
Optimal Controls ◽  
Infected Population ◽  
The Impact

We present a rigorous mathematical analysis of a deterministic model, for the transmission dynamics of hepatitis C, using a standard incidence function. The infected population is divided into three distinct compartments featuring two distinct infection stages (acute and chronic) along with an isolation compartment. It is shown that for basic reproduction number R0≤1, the disease-free equilibrium is locally and globally asymptotically stable. The model also has an endemic equilibrium for R0>1. Uncertainty and sensitivity analyses are carried out to identify and study the impact of critical parameters on R0. In addition, we have presented the numerical simulations to investigate the influence of different important parameters on R0. Since we have a locally stable endemic equilibrium, optimal control is applied to the deterministic model to reduce the total infected population. Two different optimal control strategies (vaccination and isolation) are designed to control the disease and reduce the infected population. Pontryagin’s Maximum Principle is used to characterize the optimal controls in terms of an optimality system which is solved numerically. Numerical results for the optimal controls are compared against the constant controls and their effectiveness is discussed.

scholarly journals Optimal Control Model of Tumor Treatment with Oncolytic Virus and MEK Inhibitor

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Yongmei Su ◽  
Chen Jia ◽  
Ying Chen
Keyword(s):  
Optimal Control ◽  
Cancer Cells ◽  
Oncolytic Virus ◽  
Tumor Therapy ◽  
Treatment Strategies ◽  
Optimal Strategies ◽  
Mek Inhibitor ◽  
Mitogen Activated Protein Kinase ◽  
Mitogen Activated Protein ◽  
Negative Effect

Tumors are a serious threat to human health. The oncolytic virus is a kind of tumor killer virus which can infect and lyse cancer cells and spread through the tumor, while leaving normal cells largely unharmed. Mathematical models can help us to understand the tumor-virus dynamics and find better treatment strategies. This paper gives a new mathematical model of tumor therapy with oncolytic virus and MEK inhibitor. Stable analysis was given. Because mitogen-activated protein kinase (MEK) can not only lead to greater oncolytic virus infection into cancer cells, but also limit the replication of the virus, in order to provide the best dosage of MEK inhibitors and balance the positive and negative effect of the inhibitors, we put forward an optimal control problem of the inhibitor. The optimal strategies are given by theory and simulation.

scholarly journals Optimal Control and Temperature Variations of Malaria Transmission Dynamics

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-32
Author(s):  
Folashade B. Agusto
Keyword(s):  
Optimal Control ◽  
Climatic Factors ◽  
Control Strategies ◽  
Sub Saharan Africa ◽  
Personal Protection ◽  
Temperature Dependent ◽  
Infected Female ◽  
Anopheles Mosquitoes ◽  
Geographical Regions ◽  
The Impact

Malaria is a Plasmodium parasitic disease transmitted by infected female Anopheles mosquitoes. Climatic factors, such as temperature, humidity, rainfall, and wind, have significant effects on the incidence of most vector-borne diseases, including malaria. The mosquito behavior, life cycle, and overall fitness are affected by these climatic factors. This paper presents the results obtained from investigating the optimal control strategies for malaria in the presence of temperature variation using a temperature-dependent malaria model. The study further identified the temperature ranges in four different geographical regions of sub-Saharan Africa, suitable for mosquitoes. The optimal control strategies in the temperature suitable ranges suggest, on average, a high usage of both larvicides and adulticides followed by a moderate usage of personal protection such as bednet. The average optimal bednet usage mimics the solution profile of the mosquitoes as the mosquitoes respond to changes in temperature. Following the results from the optimal control, this study also investigates using a temperature-dependent model with insecticide-sensitive and insecticide-resistant mosquitoes the impact of insecticide-resistant mosquitoes on disease burden when temperature varies. The results obtained indicate that optimal bednet usage on average is higher when insecticide-resistant mosquitoes are present. Besides, the average bednet usage increases as temperature increases to the optimal temperature suitable for mosquitoes, and it decreases after that, a pattern similar to earlier results involving insecticide-sensitive mosquitoes. Thus, personal protection, particularly the use of bednets, should be encouraged not only at low temperatures but particularly at high temperatures when individuals avoid the use of bednets. Furthermore, control and reduction of malaria may be possible even when mosquitoes develop resistance to insecticides.

scholarly journals Evidence for in vitro and in vivo activity of the antimalarial pyronaridine against Schistosoma

2021 ◽  
Vol 15 (6) ◽  
pp. e0009511
Author(s):  
Erik Koehne ◽  
Nina Zander ◽  
Miriam Rodi ◽  
Jana Held ◽  
Wolfgang Hoffmann ◽  
...  
Keyword(s):  
Methylene Blue ◽  
Antimalarial Drug ◽  
Large Scale ◽  
Ex Vivo ◽  
Pilot Trial ◽  
Treatment Strategies ◽  
Sub Saharan Africa ◽  
Highly Active

Background Schistosomiasis is highly prevalent in Africa. Praziquantel is effective against adult schistosomes but leaves prepatent stages unaffected—which is a limit to patient management and elimination. Given the large-scale use of praziquantel, development of drug resistance by Schistosoma is feared. Antimalarials are promising drugs for alternative treatment strategies of Schistosoma infections. Development of drugs with activity against both malaria and schistosomiasis is particularly appealing as schistosome infections often occur concomitantly with malaria parasites in sub-Saharan Africa. Therefore, antiplasmodial compounds were progressively tested against Schistosoma in vitro, in mice, and in a clinical study. Results Amongst 16 drugs and 1 control tested, pyronaridine, methylene blue and 5 other antimalarials were highly active in vitro against larval stage schistosomula with a 50% inhibitory concentration below 10 μM. Both drugs were lethal to ex vivo adult worms tested at 30 μM with methylene blue also active at 10 μM. Pyronaridine treatment of mice infected with S. mansoni at the prepatent stage reduced worm burden by 82% and cured 7 out of 12 animals, however in mice adult stages remained viable. In contrast, methylene blue inhibited adult worms by 60% but cure was not achieved. In an observational pilot trial in Gabon in children, the antimalarial drug combination pyronaridine-artesunate (Pyramax) reduced S. haematobium egg excretion from 10/10 ml urine to 0/10 ml urine, and 3 out of 4 children were cured. Conclusion Pyronaridine and methylene blue warrant further investigation as candidates for schistosomiasis treatment. Both compounds are approved for human use and evidence for their potential as antischistosomal compounds can be obtained directly from clinical testing. Particularly, pyronaridine-artesunate, already available as an antimalarial drug, calls for further clinical evaluation. Trial registration ClinicalTrials.gov Identifier NCT03201770.

scholarly journals Modeling and Optimal Control of a Class of Warfare Hybrid Dynamic Systems Based on Lanchester(n,1)Attrition Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiangyong Chen ◽  
Ancai Zhang
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Dynamic Systems ◽  
Control Strategies ◽  
Discrete Event ◽  
Optimal Strategies ◽  
Hybrid Dynamic System ◽  
Differential Game Theory ◽  
Case Simulation ◽  
Lanchester Equation

For the particularity of warfare hybrid dynamic process, a class of warfare hybrid dynamic systems is established based on Lanchester equation in a(n,1)battle, where a heterogeneous force ofndifferent troop types faces a homogeneous force. This model can be characterized by the interaction of continuous-time models (governed by Lanchester equation), and discrete event systems (described by variable tactics). Furthermore, an expository discussion is presented on an optimal variable tactics control problem for warfare hybrid dynamic system. The optimal control strategies are designed based on dynamic programming and differential game theory. As an example of the consequences of this optimal control problem, we take the (2, 1) case and solve the optimal strategies in a (2, 1) case. Simulation results show the feasibility of warfare hybrid system model and the effectiveness of the optimal control strategies designed.

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