scholarly journals Mathematical Modelling and Control of COVID-19 Transmission in the Presence of Exposed Immigrants

2021 ◽  
Vol 4 (2) ◽  
pp. 93-105
Author(s):  
Reuben Iortyer Gweryina ◽  
Chinwendu Emilian Madubueze ◽  
Martins Afam Nwaokolo
Keyword(s):  
Mathematical Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Horizontal Transmission ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Susceptible Population ◽  
Continuous Mixing ◽  
And Control ◽  
The Impact

In this paper, a mathematical model for COVID-19 pandemic that spreads through horizontal transmission in the presence of exposed immigrants is studied. The model has equilibrium points, notably, COVID-19-free equilibrium and COVID-19-endemic equilibrium points. The model exhibits a basic reproduction number, R0 which determines the elimination and persistence of the disease. It was found that when R0 < 1, then the equilibrium becomes locally asymptotically stable and endemic equilibrium does not exists. However, when R0 > 1, the equilibrium is found to be stable globally. This implies that continuous mixing of exposed immigrants with the susceptible population will make the eradication of COVID-19 difficult and endemic in the community. The system is also proved qualitatively to experience transcritical bifurcation close to the COVID-19-free equilibrium at the point R0 = 1. Numerically, the model is used to investigate the impact of certain other relevant parameters on the spread of COVID-19 and how to curtail their effect.

scholarly journals Mathematical Modelling on Double Quarantine Process in the Spread and Stability of Covid-19

2020 ◽  
Author(s):  
Jangyadatta Behera ◽  
Aswin Kumar Rauta ◽  
Yerra Shankar Rao ◽  
Sairam Patnaik
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Analytical Result ◽  
The Stability ◽  
The Impact ◽  
Disease Free

Abstract In this paper, a mathematical model is proposed on the spread and control of corona virus disease2019 (COVID19) to ascertain the impact of pre quarantine for suspected individuals having travel history ,immigrants and new born cases in the susceptible class following the lockdown or shutdown rules and adopted the post quarantine process for infected class. Set of nonlinear ordinary differential equations (ODEs) are generated and parameters like natural mortality rate, rate of COVID-19 induced death, rate of immigrants, rate of transmission and recovery rate are integrated in the scheme. A detailed analysis of this model is conducted analytically and numerically. The local and global stability of the disease is discussed mathematically with the help of Basic Reproduction Number. The ODEs are solved numerically with the help of Runge-Kutta 4th order method and graphs are drawn using MATLAB software to validate the analytical result with numerical simulation. It is found that both results are in good agreement with the results available in the existing literatures. The stability analysis is performed for both disease free equilibrium and endemic equilibrium points. The theorems based on Routh-Hurwitz criteria and Lyapunov function are proved .It is found that the system is locally asymptotically stable at disease free and endemic equilibrium points for basic reproduction number less than one and globally asymptotically stable for basic reproduction number greater than one. Finding of this study suggest that COVID-19 would remain pandemic with the progress of time but would be stable in the long-term if the pre and post quarantine policy for asymptomatic and symptomatic individuals are implemented effectively followed by social distancing, lockdown and containment.

scholarly journals Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model

2021 ◽  
Vol 4 (2) ◽  
pp. 125-137
Author(s):  
Dipo Aldila ◽  
Arthana Islamilova ◽  
Sarbaz H.A. Khosnaw ◽  
Bevina D. Handari ◽  
Hengki Tasman
Keyword(s):  
Mathematical Model ◽  
Infection Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Control Program ◽  
Endemic Equilibrium ◽  
Dynamic Complexity ◽  
The Impact ◽  
The Basic Reproduction Number

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field.

scholarly journals A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment

2020 ◽  
Vol 24 (5) ◽  
pp. 917-922
Author(s):  
J. Andrawus ◽  
F.Y. Eguda ◽  
I.G. Usman ◽  
S.I. Maiwa ◽  
I.M. Dibal ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Line Treatment ◽  
Second Line ◽  
Tuberculosis Transmission ◽  
Disease Free

This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results. Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point

scholarly journals Modeling and Analysis of Population Dynamics of Examination Malpractice Among Students

2018 ◽  
Author(s):  
Chinedu Obasi ◽  
Collins Obiora ◽  
Godwin Mbah ◽  
Oluseye Olawuyi
Keyword(s):  
Mathematical Model ◽  
Population Dynamics ◽  
Social Problem ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Awareness Campaign ◽  
Modeling And Analysis ◽  
The Impact ◽  
Insight Into

While examination malpractice has been a recognized social problem among students, the control of the phenomenon remains a challenge. In this study, we formulate a mathematical model describing the population dynamics of examination malpractice among students. Initial insight into the dynamics of the model is gained by analyzing some important mathematical features of the model such as the basic malpractice number. The malpractice-free equilibrium and endemic equilibrium points of the model are shown to be locally asymptotically stable when the basic malpractice number is less than unity. This result implies that examination malpractice can be totally eradicated among students when the basic malpractice number is less than unity. To understand the impact of controlling this social problem, we extend the model to incorporate awareness campaign and disciplinary measure as control strategies in curtailing the act. Our analysis reveals that incorporating control strategies have some influence in reducing examination malpractice among students. Further analysis indicates that considering both control strategies simultaneously yields a better result in reducing examination malpractice and examination malpractice will grow faster when control strategies are not introduced.

scholarly journals Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Fehaid Salem Alshammari
Keyword(s):  
Fractional Order ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sir Model ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Exponential Kernel ◽  
Disease Free ◽  
The Basic Reproduction Number

AbstractThis paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The model has two equilibrium points when the basic reproduction number $R_{0} > 1$ R 0 > 1 ; a disease-free equilibrium $E_{0}$ E 0 and a disease endemic equilibrium $E_{1}$ E 1 . The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number $R_{0} <1$ R 0 < 1 , we show that the endemic equilibrium state is locally asymptotically stable if $R_{0} > 1$ R 0 > 1 . We also prove the existence and uniqueness of the solution for the Atangana–Baleanu SIR model by using a fixed-point method. Since the Atangana–Baleanu fractional derivative gives better precise results to the derivative with exponential kernel because of having fractional order, hence, it is a generalized form of the derivative with exponential kernel. The numerical simulations are explored for various values of the fractional order. Finally, the effect of the ABC fractional-order derivative on suspected and infected individuals carefully is examined and compared with the real data.

scholarly journals Stability Analysis of SEIL Tuberculosis Epidemic Model with Logistic Growth in Susceptible Compartment

2021 ◽  
Vol 16 ◽  
pp. 1-9
Author(s):  
Joko Harianto
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Tuberculosis Disease ◽  
Disease Free ◽  
The Basic Reproduction Number

This article discusses modifications to the SEIL model that involve logistical growth. This model is used to describe the dynamics of the spread of tuberculosis disease in the population. The existence of the model's equilibrium points and its local stability depends on the basic reproduction number. If the basic reproduction number is less than unity, then there is one equilibrium point that is locally asymptotically stable. The equilibrium point is a disease-free equilibrium point. If the basic reproduction number ranges from one to three, then there are two equilibrium points. The two equilibrium points are disease-free equilibrium and endemic equilibrium points. Furthermore, for this case, the endemic equilibrium point is locally asymptotically stable.

scholarly journals Mathematical Approach to Investigate Stress due to Control Measures to Curb COVID-19

2022 ◽  
Vol 2022 ◽  
pp. 1-23
Author(s):  
James Nicodemus Paul ◽  
Silas Steven Mirau ◽  
Isambi Sailon Mbalawata
Keyword(s):  
Equilibrium Points ◽  
Rank Correlation ◽  
The Body ◽  
Endemic Equilibrium ◽  
Least Square ◽  
Control Measures ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Impact

COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number ( R 0 ) was derived by using the next-generation matrix method, which shows that, when R 0 < 1 , the disease-free equilibrium is globally asymptotically stable whereas when R 0 > 1 the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and R 0 . Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.

scholarly journals Mathematical Model of Schistosomiasis under Flood in Anhui Province

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Longxing Qi ◽  
Jing-an Cui ◽  
Tingting Huang ◽  
Fengli Ye ◽  
Longzhi Jiang
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Anhui Province ◽  
Endemic Equilibrium ◽  
Observation Data ◽  
Schistosomiasis Control ◽  
The Stability ◽  
The Impact ◽  
The Basic Reproduction Number

Based on the real observation data in Tongcheng city, this paper established a mathematical model of schistosomiasis transmission under flood in Anhui province. The delay of schistosomiasis outbreak under flood was considered. Analysis of this model shows that the disease free equilibrium is locally asymptotically stable if the basic reproduction number is less than one. The stability of the unique endemic equilibrium may be changed under some conditions even if the basic reproduction number is larger than one. The impact of flood on the stability of the endemic equilibrium is studied and the results imply that flood can destabilize the system and periodic solutions can arise by Hopf bifurcation. Finally, numerical simulations are performed to support these mathematical results and the results are in accord with the observation data from Tongcheng Schistosomiasis Control Station.

scholarly journals Kestabilan Global Endemik Model Epidemi SEIR

2014 ◽  
Vol 9 (2) ◽  
pp. 52
Author(s):  
Roni Tri Putra ◽  
Sukatik - ◽  
Sri Nita ◽  
Yandraini Yunida
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Seir Model ◽  
Stability Of Equilibrium ◽  
The Basic Reproduction Number

In this paper, it will be studied global stability endemic of equilibrium points of  a SEIR model with infectious force in latent, infected and immune period. From the model it will be found investigated the existence and its stability of points its equilibrium. The global stability of equilibrium points is depending on the value of the basic reproduction number  If   there is a unique endemic equilibrium which is globally asymptotically stable.

scholarly journals Global Stability of a SLIT TB Model with Staged Progression

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yakui Xue ◽  
Xiaohong Wang
Keyword(s):  
Mathematical Model ◽  
Latent Period ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Infectious Period ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
N Stage ◽  
Disease Free ◽  
The Basic Reproduction Number

Because the latent period and the infectious period of tuberculosis (TB) are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression (SP) model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reproduction numberR0. Moreover, ifR0≤1, the disease-free equilibriumP0is globally asymptotically stable and the disease always dies out. IfR0>1, the unique endemic equilibriumP∗is globally asymptotically stable and the disease persists at the endemic equilibrium.

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