scholarly journals Mathematical Modeling for Prediction Dynamics of the Coronavirus Disease 2019 (COVID-19) Pandemic, Quarantine Control Measures

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1404
Author(s):  
Din Prathumwan ◽  
Kamonchat Trachoo ◽  
Inthira Chaiya
Keyword(s):  
Endemic Equilibrium ◽  
Control Measures ◽  
Single Infection ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Expected Number ◽  
Susceptible Population ◽  
Proposed Model ◽  
The Stability ◽  
Disease Free

A mathematical model for forecasting the transmission of the COVID-19 outbreak is proposed to investigate the effects of quarantined and hospitalized individuals. We analyze the proposed model by considering the existence and the positivity of the solution. Then, the basic reproduction number (R0)—the expected number of secondary cases produced by a single infection in a completely susceptible population—is computed by using the next-generation matrix to carry out the stability of disease-free equilibrium and endemic equilibrium. The results show that the disease-free equilibrium is locally asymptotically stable if R0<1, and the endemic equilibrium is locally asymptotically stable if R0>1. Numerical simulations of the proposed model are illustrated. The sensitivity of the model parameters is considered in order to control the spread by intervention strategies. Numerical results confirm that the model is suitable for the outbreak that occurred in Thailand.

scholarly journals Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-21
Author(s):  
Fulgensia Kamugisha Mbabazi ◽  
Joseph Y. T. Mugisha ◽  
Mark Kimathi
Keyword(s):  
Hopf Bifurcation ◽  
Time Delays ◽  
Pneumococcal Pneumonia ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Reproduction Ratio ◽  
Transversality Conditions ◽  
The Stability ◽  
Delay Differential ◽  
Disease Free

In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratioR0is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions are proved. The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively. The analytical results are supported by numerical simulations.

Dynamics of an SIRS model with age structure and two delays

2021 ◽  
pp. 2150056
Author(s):  
Hongquan Sun ◽  
Hong Li ◽  
Jin Li ◽  
Zhangsheng Zhu
Keyword(s):  
Age Structure ◽  
Semigroup Theory ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Sirs Model ◽  
Number Formula ◽  
Two Delays ◽  
Age Structured ◽  
The Stability ◽  
Disease Free

In this paper, we propose and investigate an SIRS model with age structure and two delays. Both the infected and the recovered individuals have age structure, the infection rate (from the infective to the susceptible) and the immune loss rate (from the recovered to the susceptible) are related to two independent time delays, respectively. We prove that the proposed age structured SIRS model is well-posed by using the [Formula: see text]-semigroup theory. The basic reproduction number [Formula: see text] is given, and the unique endemic equilibrium exists when [Formula: see text], while the disease-free equilibrium always exists. A rigorous mathematical analysis for the stability of two equilibria is provided. The disease-free equilibrium is local asymptotically stable if [Formula: see text], and the endemic equilibrium is local asymptotically stable if [Formula: see text] and [Formula: see text]. Finally, we give numerical simulations to verify our results.

scholarly journals Global Dynamics of a Discrete-Time MERS-Cov Model

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 563
Author(s):  
Mahmoud H. DarAssi ◽  
Mohammad A. Safi ◽  
Morad Ahmad
Keyword(s):  
Discrete Time ◽  
Global Attractivity ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Proposed Model ◽  
Threshold Conditions ◽  
Theoretical Results ◽  
Disease Free

In this paper, we have investigated the global dynamics of a discrete-time middle east respiratory syndrome (MERS-Cov) model. The proposed discrete model was analyzed and the threshold conditions for the global attractivity of the disease-free equilibrium (DFE) and the endemic equilibrium are established. We proved that the DFE is globally asymptotically stable when R0≤1. Whenever R˜0>1, the proposed model has a unique endemic equilibrium that is globally asymptotically stable. The theoretical results are illustrated by a numerical simulation.

scholarly journals Mathematical Analysis of Malaria-Schistosomiasis Coinfection Model

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
E. A. Bakare ◽  
C. R. Nwozo
Keyword(s):  
Numerical Simulations ◽  
Endemic Equilibrium ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Mathematical Techniques ◽  
Parameter Values ◽  
The Impact ◽  
Number Of Individuals ◽  
Disease Free

We formulated and analysed a mathematical model to explore the cointeraction between malaria and schistosomiasis. Qualitative and comprehensive mathematical techniques have been applied to analyse the model. The local stability of the disease-free and endemic equilibrium was analysed, respectively. However, the main theorem shows that if RMS<1, then the disease-free equilibrium is locally asymptotically stable and the phase will vanish out of the host and if RMS>1, a unique endemic equilibrium is also locally asymptotically stable and the disease persists at the endemic steady state. The impact of schistosomiasis and its treatment on malaria dynamics is also investigated. Numerical simulations using a set of reasonable parameter values show that the two epidemics coexist whenever their reproduction numbers exceed unity. Further, results of the full malaria-schistosomiasis model also suggest that an increase in the number of individuals infected with schistosomiasis in the presence of treatment results in a decrease in malaria cases. Sensitivity analysis was further carried out to investigate the influence of the model parameters on the transmission and spread of malaria-schistosomiasis coinfection. Numerical simulations were carried out to confirm our theoretical findings.

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

2010 ◽  
Vol 03 (03) ◽  
pp. 299-312 ◽  
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 ◽  
The Basic Reproduction Number

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.

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 Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR

2019 ◽  
Vol 16 (1) ◽  
pp. 107
Author(s):  
Willyam Daniel Sihotang ◽  
Ceria Clara Simbolon ◽  
July Hartiny ◽  
Desrinawati Tindaon ◽  
Lasker Pangarapan Sinaga
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Seir Model ◽  
Rate Of Spread ◽  
The Stability ◽  
Disease Free

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.

scholarly journals Global Stability Analysis of Two-Stage Quarantine-Isolation Model with Holling Type II Incidence Function

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 350 ◽  
Author(s):  
Mohammad A. Safi
Keyword(s):  
Disease Transmission ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Control Measures ◽  
Asymptotically Stable ◽  
Two Stage ◽  
Globally Asymptotically Stable ◽  
Incidence Function ◽  
Special Case ◽  
Disease Free

A new two-stage model for assessing the effect of basic control measures, quarantine and isolation, on a general disease transmission dynamic in a population is designed and rigorously analyzed. The model uses the Holling II incidence function for the infection rate. First, the basic reproduction number ( R 0 ) is determined. The model has both locally and globally asymptotically stable disease-free equilibrium whenever R 0 < 1 . If R 0 > 1 , then the disease is shown to be uniformly persistent. The model has a unique endemic equilibrium when R 0 > 1 . A nonlinear Lyapunov function is used in conjunction with LaSalle Invariance Principle to show that the endemic equilibrium is globally asymptotically stable for a special case.

GLOBAL STABILITY IN A TUBERCULOSIS MODEL INCORPORATING TWO LATENT PERIODS

2009 ◽  
Vol 02 (03) ◽  
pp. 357-362 ◽  
Author(s):  
LUJU LIU
Keyword(s):  
Latent Period ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Short Term ◽  
Globally Asymptotically Stable ◽  
Tuberculosis Model ◽  
The Stability ◽  
Disease Free

A tuberculosis (TB) model with two latent periods, short-term latent period (E1) and long-term latent period (E2), and fast and slow progressions is analyzed. The stability of the unique endemic equilibrium of the model is proved. It turns out that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number R0 ≤ 1, and the endemic equilibrium is globally asymptotically stable if R0 > 1.

Study of an epidemic model with Z-type control

2018 ◽  
Vol 11 (07) ◽  
pp. 1850084 ◽  
Author(s):  
Sudip Samanta
Keyword(s):  
Epidemic Model ◽  
Control Mechanism ◽  
Basin Of Attraction ◽  
Endemic Equilibrium ◽  
Successful Implementation ◽  
Asymptotically Stable ◽  
Infectious Disease Outbreak ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Disease Free

In the present paper, an epidemic model with Z-type control mechanism has been proposed and analyzed to explore the disease control strategy on an infectious disease outbreak. The uncontrolled model can have a disease-free equilibrium and an endemic equilibrium. The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived. It is also observed that the disease-free equilibrium is globally asymptotically stable if [Formula: see text], whereas the endemic equilibrium is globally asymptotically stable if [Formula: see text]. The model is further improved by considering Z-control mechanism and investigated. Disease can be controlled by using Z-control while the basic reproduction of the uncontrolled system is greater than unity. The positivity conditions of the solutions are derived and the basin of attraction for successful implementation of Z-control mechanism is also investigated. To verify the analytical findings, extensive numerical simulations on the model are carried out.

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