scholarly journals Modeling the Dynamics of Coronavirus Disease Pandemic Coupled with Fear Epidemics

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Saul C. Mpeshe ◽  
Nkuba Nyerere
Keyword(s):  
Disease Control ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Reproduction Number ◽  
The Third ◽  
Modeling Approach ◽  
Second Wave ◽  
The Basic Reproduction Number ◽  
Initial Transmission

A modeling approach to investigate the dynamics of COVID-19 epidemics coupled with fear is presented in this paper. The basic reproduction number R 0 is computed and employed in analysing the effect of initial transmission and the conditions for disease control or eradication. Numerical simulations show that whenever there is an outbreak coupled with fear, the disease is likely to persist in the first two months, and after that, it will start to slow down as the recovery rate from fear increases. An increase in the number of recovered individuals lead to a rise in the number of susceptibles and consequently set off a second wave of infection in the third month of the epidemic.

scholarly journals A Data Driven Analysis and Forecast of COVID-19 Dynamics during the Third Wave Using SIRD Model in Bangladesh

COVID ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 503-517
Author(s):  
Omar Faruk ◽  
Suman Kar
Keyword(s):  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Goodness Of Fit ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Dynamics ◽  
Third Wave ◽  
The Third ◽  
The Government ◽  
The Basic Reproduction Number

In this study, we developed a compartmental SIRD model to analyze and forecast the transmission dynamics of the COVID-19 pandemic in Bangladesh during the third wave caused by the Indian delta variant. With the help of the nonlinear system of differential equations, this model can analyze the trends and provide reliable predictions regarding how the epidemic would evolve. The basic reproduction number regarding the pandemic has been determined analytically. The parameters used in this model have been estimated by fitting our model to the reported data for the months of May, June, and July 2021 and the goodness of fit of the parameter’s value has been found by the respective regression coefficients. Further, we conducted a sensitivity analysis of the basic reproduction number and observed that decreasing the transmission rate is the most significant factor in disease prevention. Our proposed model’s appropriateness for the available COVID-19 data in Bangladesh has been demonstrated through numerical simulations. According to the numerical simulation, it is evident that a rise in the transmission rate leads to a significant increase in the infected number of the population. Numerical simulations have also been performed by using our proposed model to forecast the future transmission dynamics for COVID-19 over a longer period of time. Knowledge of these forecasts may help the government in adopting appropriate measures to prepare for unforeseen situations that may arise in Bangladesh as well as to minimize detrimental impacts during the outbreak.

scholarly journals Simple MSEIR Model for Measles Transmission

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.

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

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.

scholarly journals Analysis of COVID-19 based on SEIR epidemic models in a multi-patch environment

2021 ◽  
Author(s):  
Lan Meng ◽  
Wei Zhu
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Migration Rate ◽  
Reproduction Number ◽  
Population Migration ◽  
Theoretical Results ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract In this paper, an n-patch SEIR epidemic model for the coronavirus disease 2019 (COVID-19) is presented. It is shown that there is unique disease-free equilibrium for this model. Then, the dynamic behavior is studied by the basic reproduction number. Some numerical simulations with three patches are given to validate the effectiveness of the theoretical results. The influence of quarantined rate and population migration rate on the basic reproduction number is also discussed by simulation.

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 Accounting for symptomatic and asymptomatic in a SEIR-type model of COVID-19

2020 ◽  
Vol 15 ◽  
pp. 34 ◽  
Author(s):  
Jayrold P. Arcede ◽  
Randy L. Caga-anan ◽  
Cheryl Q. Mentuda ◽  
Youcef Mammeri
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Type Model ◽  
Treatment Results ◽  
Hospital Capacity ◽  
The Usa ◽  
Using Data ◽  
The Basic Reproduction Number

A mathematical model was developed describing the dynamic of the COVID-19 virus over a population considering that the infected can either be symptomatic or not. The model was calibrated using data on the confirmed cases and death from several countries like France, Philippines, Italy, Spain, United Kingdom, China, and the USA. First, we derived the basic reproduction number, R0, and estimated the effective reproduction Reff for each country. Second, we were interested in the merits of interventions, either by distancing or by treatment. Results revealed that total and partial containment is effective in reducing the transmission. However, its duration may be long to eradicate the disease (104 days for France). By setting the end of containment as the day when hospital capacity is reached, numerical simulations showed that the duration can be reduced (up to only 39 days for France if the capacity is 1000 patients). Further, results pointed out that the effective reproduction number remains large after containment. Therefore, testing and isolation are necessary to stop the disease.

scholarly journals Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Eric Ávila-Vales ◽  
Erika Rivero-Esquivel ◽  
Gerardo Emilio García-Almeida
Keyword(s):  
Numerical Simulations ◽  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
General Incidence Rate ◽  
The Basic Reproduction Number

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form Sf(I), and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.

scholarly journals Modelling the Periodic Outbreak of Measles in Mainland China

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yuyi Xue ◽  
Xiaoe Ruan ◽  
Yanni Xiao
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Control Strategies ◽  
Mainland China ◽  
Asymptomatic Infection ◽  
Protection Measures ◽  
The Basic Reproduction Number

In mainland China, measles infection reached the lowest level in 2012 but resurged again after that with a seasonally fluctuating pattern. To investigate the phenomenon of periodic outbreak and identify the crucial parameters that play in the transmission dynamics of measles, we formulate a mathematical model incorporating periodic transmission rate and asymptomatic infection with waning immunity. We define the basic reproduction number as the threshold value to govern whether measles infection dies out or not. Fitting the reported measles cases from 2013 to 2016 to our proposed model, we estimate the basic reproduction number R0 with immunization to be 1.0077. From numerical simulations, we conclude asymptomatic infection does not cause much new infections and the key parameters affecting the transmission of measles are vaccination rate, transmission rate, and recovery rate, which suggests the public to enhance vaccination and protection measures to reduce effective contacts between susceptible and infective individuals and treat infected individuals timely. To minimize the number of infected individuals at a minimal cost, we formulate an optimal control system to design optimal control strategies. Numerical simulations show the effectiveness of optimal control strategies and recommend us to implement the control strategies as soon as possible. In particular, enhancing vaccination is especially effective in lowering the initial outbreak and making disease recurrence less likely.

DYNAMICAL MODEL OF VIVAX MALARIA INTERMITTENCE ATTACK IN VIVO

2009 ◽  
Vol 02 (04) ◽  
pp. 507-524 ◽  
Author(s):  
ZHIJUN DONG ◽  
JING-AN CUI
Keyword(s):  
Numerical Simulations ◽  
Plasmodium Vivax ◽  
Human Body ◽  
Basic Reproduction Number ◽  
Vivax Malaria ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Malaria Model ◽  
The Basic Reproduction Number

Dynamical behavior of a vivax malaria model is provided and regular recurrences of the symptoms of the tertian fever are described in the human body. We calculate the basic reproduction number R0 and explain the connection between the basic reproduction number and the parasite-threshold. If R0 < 1, then plasmodium vivax will be eliminated. If R0 > 1, then malarial parasites are survivable and there is a so called parasite-threshold. When the value of the parasites is larger than this parasite-threshold the symptoms of the tertian fever appear; otherwise, if the value of the parasites is less than this parasite-threshold the tertian fever cannot give signs of the symptoms suddenly in vivo. We illustrate that the gravity of infected baby is worse than that of infected grownup and also explain that the advancing of the vivax malaria can be arrested by eliminating malarial parasites in erythrocyte stage with clinical treatment by numerical simulations.

scholarly journals Estimating the reproduction number of COVID-19 in Iran using epidemic modeling

2020 ◽  
Author(s):  
Ebrahim Sahafizadeh ◽  
Samaneh Sartoli
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Model ◽  
The Novel ◽  
Epidemic Spreading ◽  
Social Distancing ◽  
Novel Coronavirus ◽  
And Control ◽  
Second Wave ◽  
The Basic Reproduction Number

AbstractBackgroundAs reported by Iranian governments, the first cases of coronavirus (COVID-19) infections confirmed in Qom, Iran on February 19, 2020 (30 Bahman 1398). The number of identified cases afterward increased rapidly and the novel coronavirus spread to all provinces of the country. This study aimed to fit an epidemic model to the reported cases data to estimate the basic reproduction number (R0) of COVID-19 in Iran.MethodsWe used data from February 21, 2020, to April 21, 2020, on the number of cases reported by Iranian governments and we employed the SIR (Susceptible-Infectious-Removed) epidemic spreading model to fit the transmission model to the reported cases data by tuning the parameters in order to estimate the basic reproduction number of COVID-19 in Iran.ResultsThe value of reproduction number was estimated 4.86 in the first week and 4.5 in the second week. it decreased from 4.29 to 2.37 in the next four weeks. At the seventh week of the outbreak the reproduction number was reduced below one.ConclusionsThe results indicate that the basic reproduction number of COVID-19 was significantly larger than one in the early stages of the outbreak. However, implementing social distancing and preventing travelling on Nowruz (Persian New Year) effectively reduced the reproduction number. Although the results indicate that reproduction number is below one, it is necessary to continue social distancing and control travelling to prevent causing a second wave of outbreak.

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