scholarly journals Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1564
Author(s):  
Gilberto Gonzalez-Parra ◽  
Abraham J. Arenas
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Potential Outcomes ◽  
Public Concern ◽  
Globally Asymptotically Stable ◽  
Lasalle Invariant Principle ◽  
The Mathematical Model ◽  
The Basic Reproduction Number

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number R0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

The impact of media coverage with a piecewise transmission rate in the spread of diseases

2016 ◽  
Vol 10 (01) ◽  
pp. 1750003
Author(s):  
Maoxing Liu ◽  
Lixia Zuo
Keyword(s):  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Three Dimensional ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Contact Transmission ◽  
The Impact ◽  
The Basic Reproduction Number

A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that media coverage exhibits its effect only when the number of the infected exceeds a certain critical level. Further, it is assumed that the impact of media coverage on the contact transmission is described by an exponential decreasing factor. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity and media coverage impact is sufficiently small, a unique endemic equilibrium exists, which is globally asymptotically stable.

scholarly journals Stability of a Mathematical Model of Malaria Transmission with Relapse

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
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.

scholarly journals Dynamics of A Multi-stage Epidemic Model with and without Treatment

2020 ◽  
Vol 8 (5) ◽  
pp. 5293-5300
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Dynamical Behaviour ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, a non-linear mathematical model is proposed with the thought of treatment to depict the spread of infectious illness and assessed with three contamination stages. We talk about the dynamical behaviour and analytical study of the framework for the mathematical model which shows that it has two non-negative equilibrium points i.e., disease-free equilibrium (DFE) and interior(endemic) equilibrium. The outcomes show that the dynamical behaviour of the model is totally determined by the basic reproduction number. For the basic reproduction number , the disease-free equilibrium is locally as well as globally asymptotically stable under a particular parameter set. In case , the model at the interior equilibrium is locally as well as globally asymptotically stable. Finally, numerical solutions of the model corroborate the analytical results and facilitate a sensitivity analysis of the model parameters.

scholarly journals Pemodelan Matematika SEIRS Pada Penyebaran Penyakit Malaria di Kabupaten Mimika

2021 ◽  
Vol 4 (1) ◽  
pp. 21
Author(s):  
Hisyam Ihsan ◽  
Syafruddin Side ◽  
Musdalifa Pagga
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
District Health Office ◽  
District Health ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Malaria Model ◽  
The Basic Reproduction Number

Abstrak. Penelitian ini  bertujuan untuk membangun model penyebaran pada penyakit malaria tipe SEIRS (Susceptible-Exposed- Infected- Recovered- Susceptible) dengan menambahkan parameter penanganan(pengobatan) pada kelas Exposed dan asumsi bahwa manusia yang pulih dapat rentan kembali terkena penyakit malaria. Model ini dibagi menjadi empat kelas yaitu, rentan, terinfeksi tapi belum aktif, terinfeksi, dan sembuh. Data yang digunakan adalah data jumlah penderita penyakit malaria dari Dinas Kesehatan Kabupaten Mimika tahun 2018. Model matematika tipe SEIRS digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi dari model SEIRS diperoleh bilangan reproduksi dasar  sebesar 0,09 yang menandakan bahwa penyebaran penyakit malaria tidak menyebabkan orang lain terkena penyakit malaria.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Malaria, Model SEIRSAbstract. This research aims to build a model of the spread of malaria diseases type SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) by adding treatment parameters (treatment) in the Exposed class and the assumption that humans who recover can be vulnerable to malaria again. This model is divided into four classes namely, vulnerable, infected but not yet active, infected, and cured. The data used are data on the number of malaria sufferers from the Mimika District Health Office in 2018. The mathematical model of the type SEIRS is used to determine the equilibrium point. Based on the simulation results of the SEIRS model, the basic reproduction number (R0) of 0.09 indicates that the spread of malaria does not cause others to contract malaria.Keywords: Equilibrium Point, Basic Reproductive Numbers, Malaria, SEIRS Model

scholarly journals A Mathematical Model Approach for Prevention and Intervention Measures of the COVID–19 Pandemic in Uganda

2020 ◽  
Author(s):  
Fulgensia Kamugisha Mbabazi ◽  
Yahaya Gavamukulya ◽  
Richard Awichi ◽  
Peter Olupot–Olupot ◽  
Samson Rwahwire ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Transmission Rate ◽  
Control Strategies ◽  
Social Distancing ◽  
Corona Virus ◽  
The Impact ◽  
The Basic Reproduction Number

AbstractThe human–infecting corona virus disease (COVID–19) caused by the novel severe acute respiratory syndrome corona virus 2 (SARS–CoV–2) was declared a global pandemic on March 11th, 2020. Current human deaths due to the infection have raised the threat globally with only 1 African country free of Virus (Lesotho) as of May 6th, 2020. Different countries have adopted different interventions at different stages of the outbreak, with social distancing being the first option while lock down the preferred option for flattening the curve at the peak of the pandemic. Lock down is aimed at adherence to social distancing, preserve the health system and improve survival. We propose a Susceptible–Exposed–Infected–Expected recoveries (SEIR) mathematical model to study the impact of a variety of prevention and control strategies Uganda has applied since the eruption of the pandemic in the country. We analyze the model using available data to find the infection–free, endemic/infection steady states and the basic reproduction number. In addition, a sensitivity analysis done shows that the transmission rate and the rate at which persons acquire the virus, have a positive influence on the basic reproduction number. On other hand the rate of evacuation by rescue ambulance greatly reduces the reproduction number. The results have potential to inform the impact and effect of early strict interventions including lock down in resource limited settings and social distancing.

scholarly journals Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Maoxing Liu ◽  
Yuting Chang ◽  
Lixia Zuo
Keyword(s):  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Contact Transmission ◽  
The Media ◽  
The Impact ◽  
The Basic Reproduction Number

An epidemic model with media is proposed to describe the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that the media has its effect when the number of the infected exceeds a certain critical level. Furthermore, it is assumed that the impact of the media on the contact transmission is described by an exponential function. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity, a unique endemic equilibrium exists, which is also globally asymptotically stable. Our analysis implies that media coverage plays an important role in controlling the spread of the disease.

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

2017 ◽  
Vol 10 (07) ◽  
pp. 1750096 ◽  
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.

scholarly journals An SEIQR Mathematical Model for The Spread of COVID-19

2020 ◽  
pp. 35-41
Author(s):  
Samuel B. Apima ◽  
Jacinta M. Mutwiwa
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Lyapunov Functions ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Novel Coronavirus ◽  
Disease Free ◽  
The Basic Reproduction Number

COVID-19, a novel coronavirus, is a respiratory infection which is spread between humans through small droplets expelled when a person with COVID-19 sneezes, coughs, or speaks. An SEIQR model to investigate the spread of COVID-19 was formulated and analysed. The disease free equilibrium point for formulated model was shown to be globally asymptotically stable. The endemic states were shown to exist provided that the basic reproduction number is greater than unity. By use of Routh-Hurwitz criterion and suitable Lyapunov functions, the endemic states are shown to be locally and globally asymptotically stable respectively. This means that any perturbation of the model by the introduction of infectives the model solutions will converge to the endemic states whenever reproduction number is greater than one, thus the disease transmission levels can be kept quite low or manageable with minimal deaths at the peak times of the re-occurrence.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Brenda M. Samiadji ◽  
Gracia M. Simorangkir ◽  
Sarbaz H. A. Khosnaw ◽  
Muhammad Shahzad
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccination Strategy ◽  
Vaccination Rate ◽  
Rapid Testing ◽  
Social Distancing ◽  
Rapid Spread ◽  
Vaccine Potential ◽  
The Basic Reproduction Number

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.

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