scholarly journals Effect of the Planetesimal Belt on the Dynamics of the Restricted Problem of 2 + 2 Bodies

2022 ◽  
Vol 12 (1) ◽  
pp. 424
Author(s):  
Govind Mahato ◽  
Ashok Kumar Pal ◽  
Sawsan Alhowaity ◽  
Elbaz I. Abouelmagd ◽  
Badam Singh Kushvah
Keyword(s):  
Restricted Problem ◽  
Equilibrium Points ◽  
Small Bodies ◽  
Existence And Stability ◽  
The Impact

In this paper, we study the existence and stability of collinear and noncollinear equilibrium points within the frame of the perturbed restricted problem of 2 + 2 bodies by a planetesimal belt. We compare and investigate the corresponding results of the perturbed and unperturbed models. The impact of the planetesimal belt is observed on collinear and noncollinear equilibrium points. We demonstrate that all equilibrium points are unstable, and we numerically investigate the noncollinear equilibrium points. Finally, we emphasize that the proposed problem is a credible model for describing the capture of small bodies by a planet.

MODELING VACCINE PREVENTABLE VECTOR-BORNE INFECTIONS: YELLOW FEVER AS A CASE STUDY

2016 ◽  
Vol 24 (02n03) ◽  
pp. 193-216 ◽  
Author(s):  
SILVIA MARTORANO RAIMUNDO ◽  
HYUN MO YANG ◽  
EDUARDO MASSAD
Keyword(s):  
Mortality Rate ◽  
Yellow Fever ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Vaccination Rate ◽  
Sensitivity Analyses ◽  
Existence And Stability ◽  
Vector Borne ◽  
The Impact

In this paper, we propose and simulate a deterministic model for a vector-borne disease in the presence of a vaccine. The model allows the assessment of the impact of an imperfect vaccine with various characteristics, which include waning protective immunity, incomplete vaccine-induced protection and adverse events. We find three threshold parameters which govern the existence and stability of the equilibrium points. Our stability analysis suggests that the reduction in the mosquito fertility theoretically is the most effective factor of reducing disease prevalence in both low and high transmission areas. To illustrate the theoretical results, the model is simulated by the example of yellow fever. We also perform sensitivity analyses to determine the importance of both vaccine-induced mortality rate and disease-induced mortality rate for determining a control strategy. We found that there is an optimum vaccination rate, above which people die by the vaccination and below which people die by the disease.

Bifurcation Analysis of a Prey–Predator Model with Beddington–DeAngelis Type Functional Response and Allee Effect in Prey

2020 ◽  
Vol 30 (16) ◽  
pp. 2050238
Author(s):  
Koushik Garain ◽  
Partha Sarathi Mandal
Keyword(s):  
Functional Response ◽  
Death Rate ◽  
Allee Effect ◽  
Equilibrium Points ◽  
Growth Function ◽  
Global Dynamics ◽  
Density Dependent ◽  
Existence And Stability ◽  
Predator Model ◽  
The Impact

The article aims to study a prey–predator model which includes the Allee effect phenomena in prey growth function, density dependent death rate for predators and Beddington–DeAngelis type functional response. We notice the changes in the existence and stability of the equilibrium points due to the Allee effect. To investigate the complete global dynamics of the Allee model, we present here a two-parametric bifurcation diagram which describes the effect of density dependent death rate parameter of predator on dynamical changes of the system. We have also analyzed all possible local and global bifurcations that the system could go through, namely transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, cusp bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Finally, the impact of the Allee effect in the considered system is investigated by comparing the dynamics of both the systems with and without Allee effect.

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.

scholarly journals Stability and optimal control of a delayed HIV/AIDS-PrEP model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Cristiana J. Silva
Keyword(s):  
Optimal Control ◽  
Hiv Infection ◽  
Equilibrium Points ◽  
Minimum Principle ◽  
Existence And Stability ◽  
Prep Implementation ◽  
Exposure Prophylaxis ◽  
The Impact ◽  
Number Of Individuals ◽  
Hiv Aids

<p style='text-indent:20px;'>In this paper, we propose a time-delayed HIV/AIDS-PrEP model which takes into account the delay on pre-exposure prophylaxis (PrEP) distribution and adherence by uninfected persons that are in high risk of HIV infection, and analyze the impact of this delay on the number of individuals with HIV infection. We prove the existence and stability of two equilibrium points, for any positive time delay. After, an optimal control problem with state and control delays is proposed and analyzed, where the aim is to find the optimal strategy for PrEP implementation that minimizes the number of individuals with HIV infection, with minimal costs. Different scenarios are studied, for which the solutions derived from the Minimum Principle for Multiple Delayed Optimal Control Problems change depending on the values of the time delays and the weights constants associated with the number of HIV infected individuals and PrEP. We observe that changes on the weights constants can lead to a passage from <i>bang-singular-bang</i> to <i>bang-bang</i> extremal controls.</p>

scholarly journals A Control Based Mathematical Model for the Evaluation of Intervention Lines in COVID-19 Epidemic Spread: The Italian Case Study

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 890
Author(s):  
Paolo Di Giamberardino ◽  
Rita Caldarella ◽  
Daniela Iacoviello
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Italian Case ◽  
Control Actions ◽  
Containment Measures ◽  
Asymptomatic Subjects ◽  
The Impact

This paper addresses the problem of describing the spread of COVID-19 by a mathematical model introducing all the possible control actions as prevention (informative campaign, use of masks, social distancing, vaccination) and medication. The model adopted is similar to SEIQR, with the infected patients split into groups of asymptomatic subjects and isolated ones. This distinction is particularly important in the current pandemic, due to the fundamental the role of asymptomatic subjects in the virus diffusion. The influence of the control actions is considered in analysing the model, from the calculus of the equilibrium points to the determination of the reproduction number. This choice is motivated by the fact that the available organised data have been collected since from the end of February 2020, and almost simultaneously containment measures, increasing in typology and effectiveness, have been applied. The characteristics of COVID-19, not fully understood yet, suggest an asymmetric diffusion among countries and among categories of subjects. Referring to the Italian situation, the containment measures, as applied by the population, have been identified, showing their relation with the government's decisions; this allows the study of possible scenarios, comparing the impact of different possible choices.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

scholarly journals Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students

2020 ◽  
Vol 16 (32) ◽  
pp. 195-223
Author(s):  
Edgardo Pérez
Keyword(s):  
Mathematical Modeling ◽  
College Students ◽  
Mathematical Model ◽  
Drinking Behavior ◽  
Preventive Measure ◽  
Nonlinear Mathematical Model ◽  
Consumption Behavior ◽  
Existence And Stability ◽  
Drugs And Crime ◽  
The Impact

In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.

scholarly journals Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network

2021 ◽  
Vol 19 (2) ◽  
pp. 1677-1695
Author(s):  
Boli Xie ◽  
◽  
Maoxing Liu ◽  
Lei Zhang
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Virus Transmission ◽  
Population Heterogeneity ◽  
Multiple Equilibrium ◽  
Optimal Control Strategy ◽  
Treatment Function ◽  
The Stability ◽  
The Impact

<abstract><p>In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} &lt; 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.</p></abstract>

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