A Mathematical Model to Study the Effect of Travel Between Two Regions on the Covid-19 Infections

COVID-19 has attracted a lot of researchers’ attention since it has emerged in Wuhan, China in December 2019. Numerous model predictions on the COVID-19 epidemic have been created in case of Wuhan and the other regions. In this paper, a new COVID-19 epidemic model between two regions is proposed. The model differentiates asymptomatic infectious compartment and symptomatic infectious compartment. It is assumed that the symptomatic population cannot infect the susceptible population due to direct isolation, but the asymptomatic population can. The symptomatic population is also assumed to be unable to travel between regions. We analyze the stability of the model using Lyapunov Function. The Basic Reproduction Number for the model is presented. The numerical simulation and sensitivity analysis are explored to determine the significant parameter of the model.

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MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

International Journal of Engineering Applied Sciences and Technology ◽

10.33564/ijeast.2021.v05i10.013 ◽

2021 ◽

Vol 5 (10) ◽

Author(s):

Oluwafemi Temidayo J. ◽

Azuaba E. ◽

Lasisi N. O.

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Equilibrium Point ◽

Reproduction Number ◽

Endemic Equilibrium ◽

The Mathematical Model ◽

Globally Stable ◽

Well Posed ◽

The Basic Reproduction Number ◽

Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

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Simple MSEIR Model for Measles Transmission

Asian Research Journal of Mathematics ◽

10.9734/arjom/2019/v12i330090 ◽

2019 ◽

pp. 1-11

Author(s):

Mojeeb Al-Rahman EL-Nor Osman ◽

Appiagyei Ebenezer ◽

Isaac Kwasi Adu

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Recovery Rate ◽

Birth Rate ◽

Reproduction Number ◽

Progression Rate ◽

Asymptotically Stable ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria. The basic reproduction number is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out. The disease was locally asymptotically stable if and unstable if . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

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Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

10.21203/rs.3.rs-28213/v1 ◽

2020 ◽

Author(s):

Tamer Sanlidag ◽

Nazife Sultanoglu ◽

Bilgen Kaymakamzade ◽

Evren Hincal ◽

Murat Sayan ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2 epidemic.

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Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

10.21203/rs.3.rs-28704/v1 ◽

2020 ◽

Author(s):

Tamer Sanlidag ◽

Nazife Sultanoglu ◽

Bilgen Kaymakamzade ◽

Evren Hincal ◽

Murat Sayan ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

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Mathematical Assessment of the Dynamical Model of Smoking Tobacco Epidemic in Bangladesh

International Journal of Science and Management Studies (IJSMS) ◽

10.51386/25815946/ijsms-v3i2p105 ◽

2020 ◽

pp. 36-48

Author(s):

Sk. Abdus Samad ◽

Md. Tusberul Islam ◽

Sayed Toufiq Hossain Tomal ◽

MHA Biswas

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Stability Analysis ◽

Differential Equations ◽

Basic Reproduction Number ◽

Conversion Rate ◽

Reproduction Number ◽

The World ◽

Tobacco Epidemic ◽

The Basic Reproduction Number

Bangladesh is one of the largest tobacco users in the world being troubled by smoking related issues. In this paper we consider a compartmental mathematical model of smoking in which the population is divided into five compartments: susceptible, expose, smokers, temporary quitters and permanent quitters described by ordinary differential equations. We study by including the conversion rate from light smoker to permanent quit smokers. The basic reproduction number R0 has been derived and then we found two euilibria of the model one of them is smoking-free and other of them is smoking-present. We establish the positivity, boundedness of the solutions and perform stability analysis of the model. To decrease the smoking propensity in Bangladesh we perform numerical simulation for various estimations of parameters which offer understanding to give up smoking and how they influence the smoker and exposed class. This model gives us legitimate thought regarding the explanations for the spread of smoking in Bangladesh.

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A Mathematical Model to Demonstrate the Spread of an Epidemic

GANIT Journal of Bangladesh Mathematical Society ◽

10.3329/ganit.v29i0.8522 ◽

1970 ◽

Vol 29 ◽

pp. 127-138

Author(s):

Jannatun Nayeem ◽

Kazi Aminur Rahman ◽

Md Abu Salek

Keyword(s):

Mathematical Model ◽

Infectious Diseases ◽

Reproduction Number ◽

Dimensional Model ◽

Expected Number ◽

Susceptible Population ◽

Non Linear ◽

Dynamical Method ◽

The Stability ◽

Hiv Aids

Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Non-linear dynamical method of projecting the transmission of an epidemic is accurate if the input parameters are reliable. In this paper, a mathematical model is constructed for predicting an epidemic of HIV/AIDS with respect to the presence of infected individuals in the population. For the model, a formula for the basic reproduction number, R0 (the expected number of secondary infectious caused by a single new infective introduced into a susceptible population) is determined. The six dimensional model is analyzed qualitatively to determine the stability of equilibria. Analysis of this model includes identifying the threshold R0 that determines whether the disease dies out or an epidemic occurs. Key words: Non-linear dynamical method; infectious diseases; epidemic stability; HIV/AIDS. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 127-138 DOI: http://dx.doi.org/10.3329/ganit.v29i0.8522

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Mathematical Model of Schistosomiasis under Flood in Anhui Province

Abstract and Applied Analysis ◽

10.1155/2014/972189 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 4

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.

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Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease

Abstract and Applied Analysis ◽

10.1155/2014/182680 ◽

2014 ◽

Vol 2014 ◽

pp. 1-15 ◽

Cited By ~ 1

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.

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A Mathematical Model to Investigate the Transmission of COVID-19 in the Kingdom of Saudi Arabia

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/9136157 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Fehaid Salem Alshammari

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Saudi Arabia ◽

Reproduction Number ◽

Real Data ◽

Kingdom Of Saudi Arabia ◽

Globally Stable ◽

Disease Free ◽

The Basic Reproduction Number ◽

Good Agreement

Since the first confirmed case of SARS-CoV-2 coronavirus (COVID-19) on March 02, 2020, Saudi Arabia has not reported quite a rapid COVD-19 spread as seen in America and many European countries. Possible causes include the spread of asymptomatic COVID-19 cases. To characterize the transmission of COVID-19 in Saudi Arabia, a susceptible, exposed, symptomatic, asymptomatic, hospitalized, and recovered dynamical model was formulated, and a basic analysis of the model is presented including model positivity, boundedness, and stability around the disease-free equilibrium. It is found that the model is locally and globally stable around the disease-free equilibrium when R 0 < 1 . The model parameterized from COVID-19 confirmed cases reported by the Ministry of Health in Saudi Arabia (MOH) from March 02 till April 14, while some parameters are estimated from the literature. The numerical simulation showed that the model predicted infected curve is in good agreement with the real data of COVID-19-infected cases. An analytical expression of the basic reproduction number R 0 is obtained, and the numerical value is estimated as R 0 ≈ 2.7 .

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Analysis of a Simple Vector-Host Epidemic Model with Direct Transmission

Discrete Dynamics in Nature and Society ◽

10.1155/2010/679613 ◽

2010 ◽

Vol 2010 ◽

pp. 1-12 ◽

Cited By ~ 12

Author(s):

Liming Cai ◽

Xuezhi Li

Keyword(s):

Lyapunov Function ◽

Disease Transmission ◽

Reproduction Number ◽

The Other ◽

Global Asymptotical Stability ◽

Direct Transmission ◽

Si Model ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

Vector-host epidemic models with direct transmission are proposed and analyzed. It is shown that the stability of the equilibria in the proposed models can be controlled by the basic reproduction number of the disease transmission. One model considers that the dynamics of human hosts and vectors are described by SIS and SI model, respectively, where the global asymptotical stability for the equilibria of the model is analyzed by constructing Lyapunov function, respectively. The other model considers that the dynamics of the human hosts and vectors are described by SIRS and SI model, respectively, where the global stability of the disease-free equilibrium and the persistence of the disease in the model are also analyzed, respectively.

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