scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

2020 ◽  
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

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 Preventing extinction in Rastrelliger brachysoma using an impulsive mathematical model

2021 ◽  
Vol 7 (1) ◽  
pp. 1-24
Author(s):  
Din Prathumwan ◽  
◽  
Kamonchat Trachoo ◽  
Wasan Maiaugree ◽  
Inthira Chaiya ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Population Density ◽  
Upper Bound ◽  
Existence And Uniqueness ◽  
Periodic Behavior ◽  
Toxic Environment ◽  
Pacific Mackerel ◽  
The Stability ◽  
Theoretical Results

<abstract><p>In this paper, we proposed a mathematical model of the population density of Indo-Pacific mackerel (<italic>Rastrelliger brachysoma</italic>) and the population density of small fishes based on the impulsive fishery. The model also considers the effects of the toxic environment that is the major problem in the water. The developed impulsive mathematical model was analyzed theoretically in terms of existence and uniqueness, positivity, and upper bound of the solution. The obtained solution has a periodic behavior that is suitable for the fishery. Moreover, the stability, permanence, and positive of the periodic solution are investigated. Then, we obtain the parameter conditions of the model for which Indo-Pacific mackerel conservation might be expected. Numerical results were also investigated to confirm our theoretical results. The results represent the periodic behavior of the population density of the Indo-Pacific mackerel and small fishes. The outcomes showed that the duration and quantity of fisheries were the keys to prevent the extinction of Indo-Pacific mackerel.</p></abstract>

scholarly journals A Note on COVID-19 Diagnosis Number Prediction Model in China

2021 ◽  
Author(s):  
Yi Li ◽  
Xianhong Yin ◽  
Meng Liang ◽  
Xiaoyu Liu ◽  
Meng Hao ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Future Trend ◽  
Disease Prediction ◽  
The Novel ◽  
Limited Impact ◽  
Infected People ◽  
Health Authorities ◽  
Novel Coronavirus ◽  
New Diagnosis ◽  
The Mathematical Model

Abstract Objective: In December 2019, pneumonia infected with the novel coronavirus burst in Wuhan, China. We aimed to use a mathematical model to predict number of diagnosed patients in future to ease anxiety on the emergent situation. Methods: According to all diagnosis number from WHO website and combining with the transmission mode of infectious diseases, the mathematical model was fitted to predict future trend of outbreak. Our model was based on the epidemic situation in China, which could provide referential significance for disease prediction in other countries, and provide clues for prevention and intervention of relevant health authorities. In this retrospective, all diagnosis number from Jan 21 to Feb 10, 2020 reported from China was included and downloaded from WHO website. We develop a simple but accurate formula to predict the next day diagnosis number: ，where N i is the total diagnosed patient till the i th day, and was estimated as 0.904 at Feb 10. Results: Based on this model, it is predicted that the rate of disease infection will decrease exponentially. The total number of infected people is limited; thus, the disease will have limited impact. However, new diagnosis will last to end of March. Conclusions: Through the establishment of our model, we can better predict the trend of the epidemic in China.

scholarly journals A stochastic mathematical model of two different infectious epidemic under vertical transmission

2021 ◽  
Vol 19 (3) ◽  
pp. 2179-2192
Author(s):  
Xunyang Wang ◽  
◽  
Canyun Huang ◽  
Yixin Hao ◽  
Qihong Shi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Vertical Transmission ◽  
Biological Significance ◽  
Sufficient Conditions ◽  
Discussion Section ◽  
Stochastic Permanence ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Well Posed ◽  
Theoretical Results

<abstract><p>In this study, considering the effect of environment perturbation which is usually embodied by the alteration of contact infection rate, we formulate a stochastic epidemic mathematical model in which two different kinds of infectious diseases that spread simultaneously through both horizontal and vertical transmission are described. To indicate our model is well-posed and of biological significance, we prove the existence and uniqueness of positive solution at the beginning. By constructing suitable $ Lyapunov $ functions (which can be used to prove the stability of a certain fixed point in a dynamical system or autonomous differential equation) and applying $ It\hat{o} $'s formula as well as $ Chebyshev $'s inequality, we also establish the sufficient conditions for stochastic ultimate boundedness. Furthermore, when some main parameters and all the stochastically perturbed intensities satisfy a certain relationship, we finally prove the stochastic permanence. Our results show that the perturbed intensities should be no greater than a certain positive number which is up-bounded by some parameters in the system, otherwise, the system will be surely extinct. The reliability of theoretical results are further illustrated by numerical simulations. Finally, in the discussion section, we put forward two important and interesting questions left for further investigation.</p></abstract>

scholarly journals A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ibrahim M. Hezam ◽  
Abdelaziz Foul ◽  
Adel Alrasheedi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Preventive Measures ◽  
Control Model ◽  
Model Parameters ◽  
System Of Differential Equations ◽  
Model Framework ◽  
Social Distancing ◽  
Infected People ◽  
The Cost

AbstractIn this work, we propose a new dynamic mathematical model framework governed by a system of differential equations that integrates both COVID-19 and cholera outbreaks. The estimations of the model parameters are based on the outbreaks of COVID-19 and cholera in Yemen from January 1, 2020 to May 30, 2020. Moreover, we present an optimal control model for minimizing both the number of infected people and the cost associated with each control. Four preventive measures are to be taken to control the outbreaks: social distancing, lockdown, the number of tests, and the number of chlorine water tablets (CWTs). Under the current conditions and resources available in Yemen, various policies are simulated to evaluate the optimal policy. The results obtained confirm that the policy of providing resources for the distribution of CWTs, providing sufficient resources for testing with an average social distancing, and quarantining of infected individuals has significant effects on flattening the epidemic curves.

scholarly journals A Note on COVID-19 Diagnosis Number Prediction Model in China

2020 ◽  
Author(s):  
Yi Li ◽  
Xianhong Yin ◽  
Yi Wang ◽  
Meng Liang ◽  
Xiaoyu Liu ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Prediction Model ◽  
Disease Prediction ◽  
The Novel ◽  
Prevention And Intervention ◽  
Limited Impact ◽  
Infected People ◽  
Health Authorities ◽  
Novel Coronavirus ◽  
New Diagnosis

Abstract In December 2019, pneumonia infected with the novel coronavirus burst in Wuhan, China. We aimed to use a mathematical model to predict number of diagnosed patients in future to ease anxiety on the emergent situation. Our model was based on the epidemic situation in China, which could provide referential significance for disease prediction in other countries, and provide clues for prevention and intervention of relevant health authorities. In this retrospective, all diagnosis number from Jan 21 to Feb 10, 2020 reported from China was included and downloaded from WHO website. We develop a simple but accurate formula to predict the next day diagnosis number: N_i/N_(i-1) =〖(N_(i-1)/N_(i-2) )〗^α，where Ni is the total diagnosed patient till the ith day, and α was estimated as 0.904 at Feb 10. Based on this model, it is predicted that the rate of disease infection will decrease exponentially. The total number of infected people is limited; thus, the disease will have limited impact. However, new diagnosis will last to end of March. Through the establishment of our model, we can better predict the trend of the epidemic in China.

scholarly journals A Note on COVID-19 Diagnosis Number Prediction Model in China

2020 ◽  
Author(s):  
Yi Li ◽  
Xianhong Yin ◽  
Meng Liang ◽  
Xiaoyu Liu ◽  
Meng Hao ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Scientific Information ◽  
Future Trend ◽  
The Novel ◽  
Infected People ◽  
The Public ◽  
Health Authorities ◽  
Novel Coronavirus ◽  
New Diagnosis ◽  
The Mathematical Model

AbstractImportanceTo predict the diagnosed COVID-19 patients and the trend of the epidemic in China. It may give the public some scientific information to ease the fear of the epidemic.ObjectiveIn December 2019, pneumonia infected with the novel coronavirus burst in Wuhan, China. We aimed to use a mathematical model to predict number of diagnosed patients in future to ease anxiety on the emergent situation.DesignAccording to all diagnosis number from WHO website and combining with the transmission mode of infectious diseases, the mathematical model was fitted to predict future trend of outbreak.SettingOur model was based on the epidemic situation in China, which could provide referential significance for disease prediction in other countries, and provide clues for prevention and intervention of relevant health authorities.ParticipantsIn this retrospective, all diagnosis number from Jan 21 to Feb 10, 2020 reported from China was included and downloaded from WHO website.Main Outcome(s) and Measure(s)We develop a simple but accurate formula to predict the next day diagnosis number:,where Ni is the total diagnosed patient till the ith day, and α was estimated as 0.904 at Feb 10.ResultsBased on this model, it is predicted that the rate of disease infection will decrease exponentially. The total number of infected people is limited; thus, the disease will have limited impact. However, new diagnosis will last to March.Conclusions and RelevanceThrough the establishment of our model, we can better predict the trend of the epidemic in China.

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.

scholarly journals A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 376
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

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