scholarly journals District-wise estimation of Basic reproduction number (R0) for COVID-19 in India in the initial phase

2021 ◽  
Author(s):  
Pratip Shil ◽  
Nitin M. Atre ◽  
Avinash A. Patil ◽  
Babasaheb V. Tandale ◽  
Priya Abraham
Keyword(s):  
Basic Reproduction Number ◽  
Initial Phase ◽  
Reproduction Number

THEORETICAL INVESTIGATION OF THE IMPACT ON EPIDEMIC THRESHOLD OF TRAVEL BETWEEN COMMUNITIES OF RESIDENT POPULATIONS

2013 ◽  
Vol 21 (02) ◽  
pp. 1350010 ◽  
Author(s):  
KLOT PATANARAPEELERT ◽  
D. GARCIA LOPEZ ◽  
I-MING TANG ◽  
MARC A. DUBOIS
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Initial Phase ◽  
Reproduction Number ◽  
Travel Patterns ◽  
Epidemic Threshold ◽  
Contact Patterns ◽  
Resident Populations ◽  
The Impact ◽  
The Basic Reproduction Number

During the initial phase of an epidemic, individual displacements between different regions modify the contact patterns. Understanding mobility processes and their consequences is necessary to predict the subsequent spread of the disease in order to optimize control policies. The basic reproduction number is commonly used to determine the threshold between extinction and expansion of the disease. Once it is derived for an epidemic model that includes the travel of population between distinct localities, the dependence of the diseases dynamics upon travel rates becomes explicit. In this study, we examine the effects of travel on the epidemic threshold for a model of two communities. The travel rates are treated as varying subject to two scenarios. We show theoretically that if the transmission potentials within communities are moderate, the epidemic threshold can be modified by travel. The conditions for the presence of the threshold induced by travel is determined and the critical values of travel at which the basic reproduction number is equal to one are derived. We show further that these results can also be applied to a model of three communities under specific travel patterns and that the derived basic reproduction number has a form similar to that of the two communities problem.

scholarly journals Estimation of exponential growth rate and basic reproduction number of the coronavirus disease 2019 (COVID-19) in Africa

2020 ◽  
Author(s):  
Salihu S Musa ◽  
Shi Zhao ◽  
Maggie H Wang ◽  
Abdurrazaq G Habib ◽  
Umar T Mustapha ◽  
...  
Keyword(s):  
Growth Rate ◽  
Basic Reproduction Number ◽  
Exponential Growth ◽  
Initial Phase ◽  
Reproduction Number ◽  
Exponential Growth Rate ◽  
Preparedness Planning ◽  
First Case ◽  
Exponential Growth Model ◽  
The Basic Reproduction Number

Abstract Since the first case of coronavirus disease 2019 (COVID-19) was detected on February 14, 2020, the cumulative confirmations reached 834 including 17 deaths by March 19, 2020. We analyzed the initial phase of the epidemic of COVID-19 in Africa between 1 March and 19 March 2020, by using the simple exponential growth model. We estimated the exponential growth rate as 0.22 per day (95%CI: 0.20 – 0.24), and the basic reproduction number to be 2.37 (95%CI: 2.22-2.51) based on the assumption that the exponential growth starting from 1 March, 2020. Our estimates should be useful in preparedness planning.

scholarly journals Estimation of exponential growth rate and basic reproduction number of the coronavirus disease 2019 (COVID-19) in Africa

2020 ◽  
Author(s):  
Salihu S Musa ◽  
Shi Zhao ◽  
Maggie H Wang ◽  
Abdurrazaq G Habib ◽  
Umar T Mustapha ◽  
...  
Keyword(s):  
Growth Rate ◽  
Basic Reproduction Number ◽  
Exponential Growth ◽  
Initial Phase ◽  
Reproduction Number ◽  
Initial Growth ◽  
Exponential Growth Rate ◽  
Preparedness Planning ◽  
First Case ◽  
Exponential Growth Model

Abstract Background Since the first case of coronavirus disease 2019 (COVID-19) was detected on February 14, 2020, the cumulative confirmations reached 15207 including 831 deaths by April 13, 2020. Methods We analyzed the initial phase of the epidemic of COVID-19 in Africa between 1 March and 13 April 2020, by using the simple exponential growth model.Results We estimated the exponential growth rate as 0.22 per day (95%CI: 0.20 – 0.24), and the basic reproduction number, R0, to be 2.37 (95%CI: 2.22-2.51) based on the assumption that the exponential growth starting from 1 March 2020.Conclusion The initial growth of COVID-19 cases in Africa was rapid and showed large variations across countries. Our estimates should be useful in preparedness planning. Trial registration: NA

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.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals Mathematical analysis of a within-host model of SARS-CoV-2

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bhagya Jyoti Nath ◽  
Kaushik Dehingia ◽  
Vishnu Narayan Mishra ◽  
Yu-Ming Chu ◽  
Hemanta Kumar Sarmah
Keyword(s):  
Stability Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Basic Reproduction Ratio ◽  
Viral Kinetics ◽  
Reproduction Ratio ◽  
Biological Implication ◽  
Infection Models ◽  
Kinetics Of ◽  
The Basic Reproduction Number

AbstractIn this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper “The within-host viral kinetics of SARS-CoV-2” published in (Math. Biosci. Eng. 17(4):2853–2861, 2020). Important properties of the model, like nonnegativity of solutions and their boundedness, are established. Also, we have calculated the basic reproduction number which is an important parameter in the infection models. From stability analysis of the model, it is found that stability of the biologically feasible steady states are determined by the basic reproduction number $(\chi _{0})$ ( χ 0 ) . Numerical simulations are done in order to substantiate analytical results. A biological implication from this study is that a COVID-19 patient with less than one basic reproduction ratio can automatically recover from the infection.

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