Mathematical modeling of COVID-19 spreading with asymptomatic infected and interacting peoples

Abstract In this article we propose a modified compartmental (SIR) model describing the transmission of COVID-19 in Morocco. It takes account on the asymptomatic people and the strategies involving hospital isolation of the confirmed infected person, quarantine of people contacting them, and the home containment of all population to restrict mobility. We establish a relationship between the containment control coefficient $c_0$ and the basic reproduction number $\mathcal{R}_0$. Different scenarios are tested with different values of $c_0$, for which the stability of a Disease Free Equilibrium (DFE) point is correlated with the condition linking $\mathcal{R}_0$ and $c_0$. A worst scenario in which the containment is not respected in the same way during the period of confinement leads to several peaks of pandemic. It is shown that the home containment, if lived well, played a crucial role in controlling the disease spreading.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽

10.11145/j.biomath.2021.06.147 ◽

2021 ◽

Vol 10 (1) ◽

pp. 2106147

Author(s):

Debkumar Pal ◽

D Ghosh ◽

P K Santra ◽

G S Mahapatra

Keyword(s):

Mathematical Modeling ◽

Objective Function ◽

Reproduction Number ◽

Disease Incidence ◽

Treatment Control ◽

Modeling And Analysis ◽

Proposed Model ◽

The Cost ◽

Disease Free ◽

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

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 ◽

Recovery Rate ◽

Birth Rate ◽

Reproduction Number ◽

Progression Rate ◽

Asymptotically Stable ◽

The Stability ◽

Disease Free ◽

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.

THE DYNAMICS OF A DISCRETE SEIT MODEL WITH AGE AND INFECTION AGE STRUCTURES

International Journal of Biomathematics ◽

10.1142/s1793524512600042 ◽

2012 ◽

Vol 05 (03) ◽

pp. 1260004 ◽

Cited By ~ 2

Author(s):

HUI CAO ◽

YANNI XIAO ◽

YICANG ZHOU

Keyword(s):

Reproduction Number ◽

Endemic Equilibrium ◽

Disease Spread ◽

Threshold Parameter ◽

Infection Age ◽

The Stability ◽

Globally Stable ◽

Disease Free ◽

The Basic Reproduction Number ◽

Age Structures

Age and infection age have significant influence on the transmission of infectious diseases, such as HIV/AIDS and TB. A discrete SEIT model with age and infection age structures is formulated to investigate the dynamics of the disease spread. The basic reproduction number R0 is defined and used as the threshold parameter to characterize the disease extinction or persistence. It is shown that the disease-free equilibrium is globally stable if R0 < 1, and it is unstable if R0 > 1. When R0 > 1, there exists an endemic equilibrium, and the disease is uniformly persistent. The stability of the endemic equilibrium is investigated numerically.

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 ◽

Direct Contact ◽

Ebola Virus ◽

Reproduction Number ◽

Body Fluids ◽

Endemic Equilibrium ◽

The Stability ◽

Disease Free ◽

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.

Analysis and Prediction of COVID-19 Characteristics Using a Birth-and-Death Model

10.1101/2020.06.23.20138719 ◽

2020 ◽

Author(s):

Narayanan C. Viswanath

Keyword(s):

Mathematical Modeling ◽

Infectious Diseases ◽

Explicit Expression ◽

Stationary Point ◽

Reproduction Number ◽

Sir Model ◽

Expected Number ◽

Infection Period ◽

AbstractIts spreading speed together with the risk of fatality might be the main characteristic that separates COVID-19 from other infectious diseases in our recent history. In this scenario, mathematical modeling for predicting the spread of the disease could have great value in containing the disease. Several very recent papers have contributed to this purpose. In this study we propose a birth-and-death model for predicting the number of COVID-19 active cases. It relation to the Susceptible-Infected-Recovered (SIR) model has been discussed. An explicit expression for the expected number of active cases helps us to identify a stationary point on the infection curve, where the infection ceases increasing. Parameters of the model are estimated by fitting the expressions for active and total reported cases simultaneously. We analyzed the movement of the stationary point and the basic reproduction number during the infection period up to the 20th of April 2020. These provide information about the disease progression path and therefore could be really useful in designing containment strategies.

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 ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

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.

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 ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

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 ◽

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.

STABILITY OF AN AGE-STRUCTURED SEIS EPIDEMIC MODEL WITH INFECTIVITY IN INCUBATIVE PERIOD

International Journal of Biomathematics ◽

10.1142/s1793524510001033 ◽

2010 ◽

Vol 03 (03) ◽

pp. 299-312 ◽

Cited By ~ 2

Author(s):

SHU-MIN GUO ◽

XUE-ZHI LI ◽

XIN-YU SONG

Keyword(s):

Epidemic Model ◽

Reproduction Number ◽

Endemic Equilibrium ◽

Stability Conditions ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Age Structured ◽

The Stability ◽

Disease Free ◽

In this paper, an age-structured SEIS epidemic model with infectivity in incubative period is formulated and studied. The explicit expression of the basic reproduction number R0 is obtained. It is shown that the disease-free equilibrium is globally asymptotically stable if R0 < 1, at least one endemic equilibrium exists if R0 > 1. The stability conditions of endemic equilibrium are also given.

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

Advances in Difference Equations ◽

10.1186/s13662-021-03470-1 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

F. Talay Akyildiz ◽

Fehaid Salem Alshammari

Keyword(s):

Fractional Order ◽

Reproduction Number ◽

Equilibrium Points ◽

Sir Model ◽

Endemic Equilibrium ◽

Asymptotically Stable ◽

Exponential Kernel ◽

Disease Free ◽

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.