scholarly journals Control Policy Mix in Measles Transmission Dynamics Using Vaccination, Therapy, and Treatment

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Jaharuddin ◽  
Toni Bakhtiar
Keyword(s):  
Deterministic Model ◽  
Equilibrium Points ◽  
Control Policy ◽  
Optimal Controls ◽  
Control Effort ◽  
Disease States ◽  
Vaccination Therapy ◽  
The Stability ◽  
The Cost ◽  
High Scenario

This paper considers a deterministic model for the dynamics of measles transmission in a population divided into six classes with respect to the disease states: susceptible, vaccinated, exposed, infected, treated, and recovered. First, we investigate the dynamical properties of the SVEITR model such as its equilibrium points, their stability, and parameter sensitivity by applying constant controls. Criteria for determining the stability of disease-free and endemic equilibrium points are provided in terms of basic reproduction number. The model is then extended by incorporating vaccination, therapy, and treatment rates as time-dependent control variables representing the level of coverages. Application of Pontryagin’s maximum principle provides the necessary conditions that must be satisfied for the existence of optimal controls aiming at minimization of the number of exposed and infected individuals simultaneously with the control effort. Numerical simulations that were carried out using the backward sweep method and Runge–Kutta scheme suggest that optimal controls under moderate and high scenarios can effectively reduce the cases of measles. In particular, the moderate scenario that utilizes the existing coverage level of 86% for MCV1 and 69% for MCV2 can degrade the cost functional by 47% of the low scenario. Meanwhile, high scenario that takes the 2020 target of 96% as coverage only makes a slight difference in reducing the number of exposed and infected individuals.

Fear Induced Stabilization in an Intraguild Predation Model

2020 ◽  
Vol 30 (04) ◽  
pp. 2050053
Author(s):  
Mainul Hossain ◽  
Nikhil Pal ◽  
Sudip Samanta ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Intraguild Predation ◽  
Equilibrium Points ◽  
Stable Limit ◽  
Interior Equilibrium ◽  
The Rich ◽  
The Stability ◽  
The Cost ◽  
The Impact

In the present paper, we investigate the impact of fear in an intraguild predation model. We consider that the growth rate of intraguild prey (IG prey) is reduced due to the cost of fear of intraguild predator (IG predator), and the growth rate of basal prey is suppressed due to the cost of fear of both the IG prey and the IG predator. The basic mathematical results such as positively invariant space, boundedness of the solutions, persistence of the system have been investigated. We further analyze the existence and local stability of the biologically feasible equilibrium points, and also study the Hopf-bifurcation analysis of the system with respect to the fear parameter. The direction of Hopf-bifurcation and the stability properties of the periodic solutions have also been investigated. We observe that in the absence of fear, omnivory produces chaos in a three-species food chain system. However, fear can stabilize the chaos thus obtained. We also observe that the system shows bistability behavior between IG prey free equilibrium and IG predator free equilibrium, and bistability between IG prey free equilibrium and interior equilibrium. Furthermore, we observe that for a suitable set of parameter values, the system may exhibit multiple stable limit cycles. We perform extensive numerical simulations to explore the rich dynamics of a simple intraguild predation model with fear effect.

scholarly journals Stochastic analysis of a prey–predator model with herd behaviour of prey

2016 ◽  
Vol 21 (3) ◽  
pp. 345-361 ◽  
Author(s):  
Shyam Pada Bera ◽  
Alakes Maiti ◽  
Guruprasad Samanta
Keyword(s):  
Birth Rate ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Social Activity ◽  
Statistical Linearization ◽  
Predator Species ◽  
The Social ◽  
Predator Model ◽  
The Stability ◽  
White Noises

In nature, a number of populations live in groups. As a result when predators attack such a population the interaction occur only at the outer surface of the herd. Again, every model in biology, being concerned with a subsystem of the real world, should include the effect of random fluctuating environment. In this paper, we study a prey–predator model in deterministic and stochastic environment. The social activity of the prey population has been incorporated by using the square root of prey density in the functional response. A brief analysis of the deterministic model including the stability of equilibrium points is presented. In random environment, the birth rate of prey species and death rate of predator species are perturbed by Gaussian white noises. We have used the method of statistical linearization to study the stability and non-equilibrium fluctuation of the populations in stochastic model. Numerical computations carried out to illustrate the analytical findings. The biological implications of analytical and numerical findings are discussed critically.

scholarly journals Dynamics of an Epidemic Model under the Influence of Environmental Stress

2021 ◽  
Vol 16 (2) ◽  
pp. 201-243
Author(s):  
Sangeeta Saha ◽  
Guruprasad Samanta
Keyword(s):  
Environmental Stress ◽  
Environmental Pollution ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Dynamical Behaviour ◽  
Treatment Policy ◽  
The Stability ◽  
The Cost ◽  
The Impact

We have considered a compartmental epidemiological model with infectious disease to observe the influence of environmental stress on disease transmission. The proposed model is well-defined as the population at each compartment remains positive and bounded with time. Dynamical behaviour of the model is observed by the stability and bifurcation analysis at the equilibrium points. Also, numerical simulation supports the theoretical proofs and the result shows that the system undergoes a forward bifurcation around the disease-free equilibrium. Our results indicate that with the increase of environmental pollution, the overall infected population increases. Also, the disease transmission rate among the susceptible and stressed population from asymptomatically infected individuals plays a crucial role to make a system endemic. A corresponding optimal control problem has also been proposed to control the disease prevalence as well as to minimize the cost by choosing the vaccination policy before being infected and treatment policy to the infected as control variables. Numerical figures indicate that the vaccination provided to susceptible needs some time to reduce the disease transmission but the vaccination provided to stressed individuals works immediately after implementation. The treatment policy for symptomatically infected individuals works with a higher rate at an earlier stage but the intensity decreases with time. Simultaneous implementation of all control interventions is more useful to reduce the size of overall infective individuals and also to minimize the economic burden. Hence, this research clearly expresses the impact of environmental pollution (specifically the influence of environmental stress) on the disease transmission in the population.

scholarly journals Dedicated Nonlinear Control of Robot Manipulators in the Presence of External Vibration and Uncertain Payload

Robotics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 2
Author(s):  
Mustafa M. Mustafa ◽  
Ibrahim Hamarash ◽  
Carl D. Crane
Keyword(s):  
Tracking Control ◽  
Robot Manipulators ◽  
Control Design ◽  
Joint Space ◽  
Accuracy Control ◽  
Control Effort ◽  
Boundedness Property ◽  
External Vibration ◽  
The Stability ◽  
The Cost

Robot manipulators are often tasked with working in environments with vibrations and are subject to load uncertainty. Providing an accurate tracking control design with implementable torque input for these robots is a complex topic. This paper presents two approaches to solve this problem. The approaches consider joint space tracking control design in the presence of nonlinear uncertain torques caused by external vibration and payload variation. The properties of the uncertain torques are used in both approaches. The first approach is based on the boundedness property, while the second approach considers the differentiability and boundedness together. The controllers derived from each approach differ from the perspectives of accuracy, control effort, and disturbance properties. A Lyapunov-based analysis is utilized to guarantee the stability of the control design in each case. Simulation results validate the approaches and demonstrate the performance of the controllers. The derived controllers show stable results at the cost of the mentioned properties.

scholarly journals Cost-effectiveness analysis on measles transmission with vaccination and treatment intervention

2021 ◽  
Vol 6 (11) ◽  
pp. 12491-12527
Author(s):  
Shinta A. Rahmayani ◽  
◽  
Dipo Aldila ◽  
Bevina D. Handari
Keyword(s):  
Medical Treatment ◽  
Optimal Strategy ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Cost Effective ◽  
Qualitative Behaviour ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Effective Analysis

<abstract><p>A deterministic model which describes measles' dynamic using newborns and adults first and second dose of vaccination and medical treatment is constructed in this paper. Mathematical analysis about existence of equilibrium points, basic reproduction number, and bifurcation analysis conducted to understand qualitative behaviour of the model. For numerical purposes, we estimated the parameters' values of the model using monthly measles data from Jakarta, Indonesia. Optimal control theory was applied to investigate the optimal strategy in handling measles spread. The results show that all controls succeeded in reducing the number of infected individuals. The cost-effective analysis was conducted to determine the best strategy to reduce number of infected individuals with the lowest cost of intervention. Our result indicates that the use of the first dose measles vaccine with medical treatment is the most optimal strategy to control measles transmission.</p></abstract>

scholarly journals Modeling the Impact of Vaccination, Screening, Treatment on the Dynamics of Pneumonia

2020 ◽  
Vol 12 (4) ◽  
pp. 525-536
Author(s):  
K. S. Rahman ◽  
S. R. Mitkari ◽  
S. Shaikh
Keyword(s):  
Equilibrium Point ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Infected Individual ◽  
Nonlinear Ordinary Differential Equation ◽  
Endemic Equilibrium ◽  
Natural Immunity ◽  
The Stability ◽  
The Impact

In this paper we have presented a deterministic model for pneumonia transmission and we have used the model to avail the potential impact of therapy. The model is based on the vaccinated-susceptible-carrier-infected-recovered-susceptible compartmental structure and their possible interventions with the possibility of infected individual recovery from natural immunity. Here, we have modeled Pneumonia considering vaccination, screening and treatment with a system of nonlinear ordinary differential equation. The model reproduction number R0 is derived and the stability of the equilibria are derived. The stability of equilibrium points is analyzed. The results shows that there exists a locally stable disease free equilibrium points, E0 when R0<1 and a unique endemic equilibrium E1, when R0>1. Infection free point was found to be locally stable and if reproduction number is greater than unity, then there is unique endemic equilibrium point and if it is less than unity, the endemic equilibrium point is globally asymptotically stable and pneumonia will be eliminated.

Four-party evolutionary game analysis of supervision for vaccine quality in major epidemics

2022 ◽  
pp. 1-20
Author(s):  
Rongjian Xie ◽  
Yucai Jia ◽  
Yuanmei Wu ◽  
Peiyun Zhang
Keyword(s):  
Equilibrium Points ◽  
Evolutionary Game ◽  
Regulatory System ◽  
External Information ◽  
The Public ◽  
Leading Role ◽  
Government Supervision ◽  
The Government ◽  
The Stability ◽  
The Cost

During major epidemics, monitoring vaccine quality can ensure the public health and social stability. Considering that social media has become an important way for the public to obtain external information during the epidemic. We developed a dual regulatory system of vaccine quality with the government in the leading role and the participation of We Media, and constructed a four-party evolutionary game model (government regulatory agency, We Media, vaccine industry groups, and the public) and analyzed the stability of each game player’s strategy choice. The system’s possible equilibrium points are identified using Lyapunov’s first law. Then the game trajectory between stakeholders is simulated by MATLAB, the effects of initial intention and parameters on the evolution process and results are analyzed. The results show that to ensure the quality and safety of vaccines and stabilize network public opinion during epidemics, the government should invest in an effective supervision mechanism. By strengthening responsibility, increasing penalties, and reducing supervision costs, the probability of vaccine industry groups providing high-quality vaccines is effectively enhanced. Restricting the behavior of We Media and supervising vaccine industry groups to reduce speculation reduces the cost of government supervision and improves its efficiency.

scholarly journals Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls

2020 ◽  
Vol 12 (7) ◽  
pp. 2767 ◽  
Author(s):  
Víctor Yepes ◽  
José V. Martí ◽  
José García
Keyword(s):  
Black Hole ◽  
Sustainable Design ◽  
Retaining Walls ◽  
The Other ◽  
Trade Off ◽  
Construction Company ◽  
Geometric Variables ◽  
The Stability ◽  
The Cost ◽  
Black Hole Algorithm

The optimization of the cost and CO 2 emissions in earth-retaining walls is of relevance, since these structures are often used in civil engineering. The optimization of costs is essential for the competitiveness of the construction company, and the optimization of emissions is relevant in the environmental impact of construction. To address the optimization, black hole metaheuristics were used, along with a discretization mechanism based on min–max normalization. The stability of the algorithm was evaluated with respect to the solutions obtained; the steel and concrete values obtained in both optimizations were analyzed. Additionally, the geometric variables of the structure were compared. Finally, the results obtained were compared with another algorithm that solved the problem. The results show that there is a trade-off between the use of steel and concrete. The solutions that minimize CO 2 emissions prefer the use of concrete instead of those that optimize the cost. On the other hand, when comparing the geometric variables, it is seen that most remain similar in both optimizations except for the distance between buttresses. When comparing with another algorithm, the results show a good performance in optimization using the black hole algorithm.

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals Longevity of Raw and Lyophilized Crude Urease Extracts

2021 ◽  
Vol 2 (2) ◽  
pp. 325-334
Author(s):  
Neda Javadi ◽  
Hamed Khodadadi Tirkolaei ◽  
Nasser Hamdan ◽  
Edward Kavazanjian
Keyword(s):  
Crude Extract ◽  
Room Temperature ◽  
Low Cost ◽  
Extraction Process ◽  
Crude Extracts ◽  
Simple Extraction ◽  
Commercial Applications ◽  
Stable Source ◽  
The Stability ◽  
The Cost

The stability (longevity of activity) of three crude urease extracts was evaluated in a laboratory study as part of an effort to reduce the cost of urease for applications that do not require high purity enzyme. A low-cost, stable source of urease will greatly facilitate engineering applications of urease such as biocementation of soil. Inexpensive crude extracts of urease have been shown to be effective at hydrolyzing urea for carbonate precipitation. However, some studies have suggested that the activity of a crude extract may decrease with time, limiting the potential for its mass production for commercial applications. The stability of crude urease extracts shown to be effective for biocementation was studied. The crude extracts were obtained from jack beans via a simple extraction process, stored at room temperature and at 4 ℃, and periodically tested to evaluate their stability. To facilitate storage and transportation of the extracted enzyme, the longevity of the enzyme following freeze drying (lyophilization) to reduce the crude extract to a powder and subsequent re-hydration into an aqueous solution was evaluated. In an attempt to improve the shelf life of the lyophilized extract, dextran and sucrose were added during lyophilization. The stability of purified commercial urease following rehydration was also investigated. Results of the laboratory tests showed that the lyophilized crude extract maintained its activity during storage more effectively than either the crude extract solution or the rehydrated commercial urease. While incorporating 2% dextran (w/v) prior to lyophilization of the crude extract increased the overall enzymatic activity, it did not enhance the stability of the urease during storage.

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