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

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-2epidemic.

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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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DINAMIKA LOKAL MODEL EPIDEMI SVIR DENGAN IMIGRASI PADA KOMPARTEMEN VAKSINASI

BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN ◽

10.30598/barekengvol14iss2pp297-304 ◽

2020 ◽

Vol 14 (2) ◽

pp. 297-304

Author(s):

Joko Harianto ◽

Titik Suparwati ◽

Inda Puspita Sari

Keyword(s):

Equilibrium Point ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Asymptotically Stable ◽

Mathematical Epidemiology ◽

Unique Equilibrium ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

Abstrak Artikel ini termasuk dalam ruang lingkup matematika epidemiologi. Tujuan ditulisnya artikel ini untuk mendeskripsikan dinamika lokal penyebaran suatu penyakit dengan beberapa asumsi yang diberikan. Dalam pembahasan, dianalisis titik ekuilibrium model epidemi SVIR dengan adanya imigrasi pada kompartemen vaksinasi. Dengan langkah pertama, model SVIR diformulasikan, kemudian titik ekuilibriumnya ditentukan, selanjutnya, bilangan reproduksi dasar ditentukan. Pada akhirnya, kestabilan titik ekuilibirum yang bergantung pada bilangan reproduksi dasar ditentukan secara eksplisit. Hasilnya adalah jika bilangan reproduksi dasar kurang dari satu maka terdapat satu titik ekuilbirum dan titik ekuilbrium tersebut stabil asimtotik lokal. Hal ini berarti bahwa dalam kondisi tersebut penyakit akan cenderung menghilang dalam populasi. Sebaliknya, jika bilangan reproduksi dasar lebih dari satu, maka terdapat dua titik ekuilibrium. Dalam kondisi ini, titik ekuilibrium endemik stabil asimtotik lokal dan titik ekuilibrium bebas penyakit tidak stabil. Hal ini berarti bahwa dalam kondisi tersebut penyakit akan tetap ada dalam populasi. Kata Kunci : Model SVIR, Stabil Asimtotik Lokal Abstract This article is included in the scope of mathematical epidemiology. The purpose of this article is to describe the dynamics of the spread of disease with some assumptions given. In this paper, we present an epidemic SVIR model with the presence of immigration in the vaccine compartment. First, we formulate the SVIR model, then the equilibrium point is determined, furthermore, the basic reproduction number is determined. In the end, the stability of the equilibrium point is determined depending on the number of basic reproduction. The result is that if the basic reproduction number is less than one then there is a unique equilibrium point and the equilibrium point is locally asymptotically stable. This means that in those conditions the disease will tend to disappear in the population. Conversely, if the basic reproduction number is more than one, then there are two equilibrium points. The endemic equilibrium point is locally asymptotically stable and the disease-free equilibrium point is unstable. This means that in those conditions the disease will remain in the population. Keywords: SVIR Model, Locally Asymptotically stable.

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Rotavirus diarrhea – An analysis through epidemic modeling

Journal of Biomedical Engineering and Informatics ◽

10.5430/jbei.v4n2p21 ◽

2018 ◽

Vol 4 (2) ◽

pp. 21

Author(s):

Ojaswita Chaturvedi ◽

Edward Lungu ◽

Mandu Jeffrey ◽

Shedden Masupe

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Analysis Model ◽

Epidemic Modeling ◽

Model Fidelity ◽

The Stability ◽

Rotavirus Diarrhea ◽

Disease Free ◽

The Basic Reproduction Number

Modelling an infectious disease like diarrhea improves the understanding of the transmission and helps in preventing it. Based on the pathogenesis, this research creates a continuous mathematical model for diarrhea (forming an SIRS system) caused by the virus rotavirus. Basic calculations including the basic reproduction number (R0) and disease-free state are successfully completed for the described system. Results show that if the basic reproduction number is kept below 1 (i.e. R0 < 1), there will be no epidemic. This mathematical model has been simulated using assumed values of parameters to test its fidelity. In order to establish the model in a functioning form, the Routh Hurwitz method has been used for the stability analysis. Model fidelity has been made stronger by conducting the sensitivity analysis and parameter estimation too. This model is very useful and has been integrated to form utilizable systems which function as a predictive system to assist in prevention of further infections of rotavirus causing diarrhea.

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Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology

International Journal of Biomathematics ◽

10.1142/s1793524517500966 ◽

2017 ◽

Vol 10 (07) ◽

pp. 1750096 ◽

Cited By ~ 5

Author(s):

Muhammad Altaf Khan ◽

Yasir Khan ◽

Taj Wali Khan ◽

Saeed Islam

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Endemic Equilibrium ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For [Formula: see text], the disease-free equilibrium is stable both locally and globally and for [Formula: see text], the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are presented.

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On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

Applied Sciences ◽

10.3390/app10228296 ◽

2020 ◽

Vol 10 (22) ◽

pp. 8296 ◽

Cited By ~ 1

Author(s):

Malen Etxeberria-Etxaniz ◽

Santiago Alonso-Quesada ◽

Manuel De la Sen

Keyword(s):

Equilibrium Point ◽

Basic Reproduction Number ◽

Epidemic Model ◽

Disease Transmission ◽

Reproduction Number ◽

Equilibrium Points ◽

Endemic Equilibrium ◽

Impulsive Vaccination ◽

Disease Free ◽

The Basic Reproduction Number

This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

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Pengembangan Model Matematika SIRD (Susceptibles-Infected-Recovery-Deaths) Pada Penyebaran Virus Ebola

Jurnal Fourier ◽

10.14421/fourier.2016.51.23-34 ◽

2016 ◽

Vol 5 (1) ◽

pp. 23

Author(s):

Endah Purwati ◽

Sugiyanto Sugiyanto

Keyword(s):

Equilibrium Point ◽

Basic Reproduction Number ◽

Direct Contact ◽

Ebola Virus ◽

Reproduction Number ◽

Body Fluids ◽

Endemic Equilibrium ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

Ebola is a deadly disease caused by a virus and is spread through direct contact with blood or body fluids such as urine, feces, breast milk, saliva and semen. In this case, direct contact means that the blood or body fluids of patients were directly touching the nose, eyes, mouth, or a wound someone open. In this paper examined two mathematical models SIRD (Susceptibles-Infected-Recovery-Deaths) the spread of the Ebola virus in the human population. Both the mathematical model SIRD on the spread of the Ebola virus is a model by Abdon A. and Emile F. D. G. and research development model. This study was conducted to determine the point of disease-free equilibrium and endemic equilibrium point and stability analysis of the dots, knowing the value of the basic reproduction number (R0) and a simulation model using Matlab software version 6.1.0.450. From the analysis of the two models, obtained the same point for disease-free equilibrium point with the stability of different points and different points for endemic equilibrium point with the stability of both the same point and the same value to the value of the basic reproduction number (R0). After simulating the model using Matlab software version 6.1.0.450, it can be seen changes in the behavior of the population at any time.

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Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

Jambura Journal of Biomathematics (JJBM) ◽

10.34312/jjbm.v2i2.10483 ◽

2021 ◽

Vol 2 (2) ◽

pp. 68-79

Author(s):

Muhammad Manaqib ◽

Irma Fauziah ◽

Eti Hartati

Keyword(s):

Numerical Simulations ◽

Equilibrium Point ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Endemic Equilibrium ◽

Reproduction Numbers ◽

Geometric Picture ◽

Disease Free ◽

The Basic Reproduction Number

This study developed a model for the spread of COVID-19 disease using the SIR model which was added by a health mask and quarantine for infected individuals. The population is divided into six subpopulations, namely the subpopulation susceptible without a health mask, susceptible using a health mask, infected without using a health mask, infected using a health mask, quarantine for infected individuals, and the subpopulation to recover. The results obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point, and the basic reproduction number (R0). The existence of a disease-free equilibrium point is unconditional, whereas an endemic equilibrium point exists if the basic reproduction number is more than one. Stability analysis of the local asymptotically stable disease-free equilibrium point when the basic reproduction number is less than one. Furthermore, numerical simulations are carried out to provide a geometric picture related to the results that have been analyzed. The results of numerical simulations support the results of the analysis obtained. Finally, the sensitivity analysis of the basic reproduction numbers carried out obtained four parameters that dominantly affect the basic reproduction number, namely the rate of contact of susceptible individuals with infection, the rate of health mask use, the rate of health mask release, and the rate of quarantine for infected individuals.

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Stability of a Mathematical Model of Malaria Transmission with Relapse

Abstract and Applied Analysis ◽

10.1155/2014/289349 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 5

Author(s):

Hai-Feng Huo ◽

Guang-Ming Qiu

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Recovery Rate ◽

Reproduction Number ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Next Generation Matrix ◽

The Government ◽

Disease Free ◽

The Basic Reproduction Number

A more realistic mathematical model of malaria is introduced, in which we not only consider the recovered humans return to the susceptible class, but also consider the recovered humans return to the infectious class. The basic reproduction numberR0is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable ifR0≤1, and the system is uniformly persistence ifR0>1. Some numerical simulations are also given to explain our analytical results. Our results show that to control and eradicate the malaria, it is very necessary for the government to decrease the relapse rate and increase the recovery rate.

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On Oscillatory Pattern of Malaria Dynamics in a Population with Temporary Immunity

Computational and Mathematical Methods in Medicine ◽

10.1080/17486700701529002 ◽

2007 ◽

Vol 8 (3) ◽

pp. 191-203 ◽

Cited By ~ 11

Author(s):

J. Tumwiine ◽

J. Y. T. Mugisha ◽

L. S. Luboobi

Keyword(s):

Steady State ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Oscillatory Pattern ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number ◽

Temporary Immunity

We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number,R0is less than unity. We also note that whenR0>1, the disease-free equilibrium is unstable and the endemic equilibrium is stable. Numerical simulations show that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state.

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