An early estimation of the number of affected people in South Asia due to Covid-19 pandemic using susceptible, infected and recover model

2020 ◽  
Vol 31 (10) ◽  
pp. 2050140
Author(s):  
Md. Enamul Hoque
Keyword(s):  
Simple Model ◽  
South Asia ◽  
South Asian ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Sir Model ◽  
Asian Countries ◽  
Susceptible Population ◽  
The Basic Reproduction Number

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for Bangladesh, India, Pakistan and compared with that of China. Numerical solutions are used to obtain the value of parameters for the SIR model. It is predicted that the active case in Pakistan due to the SARS-CoV-2 will be comparable with that in China whereas it will be low for Bangladesh and India. The basic reproduction number, with fluctuations, for South Asian countries are predicted to be less than that of China. The susceptible population is also estimated to be under a million for Bangladesh and India but it becomes very large for Pakistan.

Estimation of the number of affected people due to the Covid-19 pandemic using susceptible, infected and recover model

2020 ◽  
Vol 31 (08) ◽  
pp. 2050111
Author(s):  
Md. Enamul Hoque
Keyword(s):  
Simple Model ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Sir Model

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for various infected countries. Numerical solutions are used to obtain the value of parameters for the SIR model. The maximum and minimum basic reproduction number (14.5 and 2.3) are predicted to be in Turkey and China, respectively.

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.

Evolution of SARS-CoV-2 in the state of Alagoas-Brazil via an adaptive SIR model

2020 ◽  
pp. 2150040
Author(s):  
I. F. F. Dos Santos ◽  
G. M. A. Almeida ◽  
F. A. B. F. De Moura
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Sir Model ◽  
The State ◽  
Epidemic Dynamics ◽  
Historical Series ◽  
Input Parameters ◽  
Number Formula ◽  
Near Future ◽  
The Basic Reproduction Number

We investigate the spreading of SARS-CoV-2 in the state of Alagoas, northeast of Brazil, via an adaptive susceptible-infected-removed (SIR) model featuring dynamic recuperation and propagation rates. Input parameters are defined based on data made available by Alagoas Secretary of Health from April 19, 2020 on. We provide with the evolution of the basic reproduction number [Formula: see text] and reproduce the historical series of the number of confirmed cases with less than [Formula: see text] error. We offer predictions, from November 16 forward, over the epidemic situation in the near future and show that it will keep decelerating. Furthermore, the same model can be used to study the epidemic dynamics in other countries with great easiness and accuracy.

scholarly journals A prototype vaccination model for endemic Covid-19 under waning immunity and imperfect vaccine take-up

2021 ◽  
Author(s):  
John S Dagpunar ◽  
ChenChen Wu
Keyword(s):  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Vaccine Coverage ◽  
Infection Prevalence ◽  
State Variables ◽  
Susceptible Population ◽  
Waning Immunity ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, for an infectious disease such as Covid-19, we present a SIR model which examines the impact of waning immunity, vaccination rates, vaccine efficacy, and the proportion of the susceptible population who aspire to be vaccinated. Under an assumed constant control reproduction number, we provide simple conditions for the disease to be eliminated, and conversely for it to exhibit the more likely endemic behaviour. With regard to Covid-19, it is shown that if the control reproduction number is set to the basic reproduction number (say 6) of the dominant delta (B1.617.2) variant, vaccination alone, even under the most optimistic of assumptions about vaccine efficacy and high vaccine coverage, is very unlikely to lead to elimination of the disease. The model is not intended to be predictive but more an aid to understanding the relative importance of various biological and control parameters. For example, from a long-term perspective, it may be found that in the UK, through changes in societal behaviour (such as mask use, ventilation, and level of homeworking), without formal government interventions such as on-off lockdowns, the control reproduction number can still be maintained at a level significantly below the basic reproduction number. Even so, our simulations show that endemic behaviour ensues. The model obtains equilibrium values of the state variables such as the infection prevalence and mortality rate under various scenarios.

scholarly journals Global Stability and Sensitivity Assessment of COVID-19 with Timely and Delayed Diagnosis in Ghana

2021 ◽  
Author(s):  
Stephen E. Moore ◽  
Hetsron L. Nyandjo Bamen ◽  
Joshua Kiddy K. Asamoah ◽  
Olivier Menoukeu-Pamen ◽  
Zhen Jin
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Delayed Diagnosis ◽  
Rank Correlation ◽  
Health Benefit ◽  
Recruitment Rate ◽  
Susceptible Population ◽  
Sensitivity Assessment ◽  
Reported Data ◽  
The Basic Reproduction Number

Abstract In this paper, we present the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana, using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, R_0, for the proposed model is 1.04. One of the main focus of this study is stability results and senesitity assessment of the parameters. We show both theoretically and numerically that, the disease can be eliminated when the basic reproduction number is less or equal to a unity. Furthermore, we show that the disease persist whenever R_0>1 or whenever there is a delay in the diagnoses of infected individuals in the community. To assess the most influential parameters in the basic reproduction number, we carried out global sensitivity analysis. The scatter plots and the partial rank correlation coefficient reveal that, the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility of exposed individuals; and that the most negative sensitive parameters are the proportion of the infectious with timely diagnosis, and the transition rate of self-quarantined individuals to the susceptible population. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection).

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

2020 ◽  
Author(s):  
Narayanan C. Viswanath
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Explicit Expression ◽  
Basic Reproduction Number ◽  
Stationary Point ◽  
Reproduction Number ◽  
Sir Model ◽  
Expected Number ◽  
Infection Period ◽  
The Basic Reproduction Number

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.

scholarly journals An Age and Space Structured SIR Model Describing the Covid-19 Pandemic

2020 ◽  
Author(s):  
Rinaldo M Colombo ◽  
Mauro Garavello ◽  
Francesca Marcellini ◽  
Elena Rossi
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Sir Model ◽  
Qualitative Properties ◽  
Numerical Integrations ◽  
Key Features ◽  
Virus Spreading ◽  
The Basic Reproduction Number

We present an epidemic model capable of describing key features of the present Covid-19 pandemic. While capturing several qualitative properties of the virus spreading, it allows to compute the basic reproduction number, the number of deaths due to the virus and various other statistics. Numerical integrations are used to illustrate the relevance of quarantine and the role of care houses.

scholarly journals The pluses and minuses of 0

2007 ◽  
Vol 4 (16) ◽  
pp. 949-961 ◽  
Author(s):  
M.G Roberts
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Central Place ◽  
Sir Model ◽  
Direct Measure ◽  
Control Effort ◽  
Epidemic Theory ◽  
The Basic Reproduction Number

The concept of the basic reproduction number ( 0 ) occupies a central place in epidemic theory. The value of 0 determines the proportion of the population that becomes infected over the course of a (modelled) epidemic. In many models, (i) an endemic infection can persist only if 0 >1, (ii) the value of 0 provides a direct measure of the control effort required to eliminate the infection, and (iii) pathogens evolve to maximize their value of 0 . These three statements are not universally true. In this paper, some exceptions to them are discussed, based on the extensions of the SIR model.

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

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Fehaid Salem Alshammari
Keyword(s):  
Fractional Order ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sir Model ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Exponential Kernel ◽  
Disease Free ◽  
The Basic Reproduction Number

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.

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