Early real-time estimation of the basic reproduction number of emerging or reemerging infectious diseases in a community with heterogeneous contact pattern: Using data from Hong Kong 2009 H1N1 Pandemic Influenza as an illustrative example

SUMMARYIn order to determine the prevalence of antibody against 2009 H1N1 influenza in Beijing, we conducted a serological survey in 710 subjects, 1 month after the epidemic peak. We found that 13·8% of our cohort was seropositive. Subjects aged ⩾60 years recorded the lowest seroprevalence (4·5%). The age-weighted seroprevalence of 14·0% was far lower than the supposed infection rate at the epidemic peak, derived from the basic reproduction number for 2009 H1N1 virus. For subjects who had received the pandemic vaccine seroprevalence was 51·4%. In subjects aged ⩾60 years the seasonal influenza vaccination was not significantly associated with being seropositive. Our study suggests that many factors, and not just the immunological level against 2009 H1N1 influenza in the community, affected the spread of the virus within the population of Beijing.

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

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2020021 ◽

2020 ◽

Vol 15 ◽

pp. 34 ◽

Cited By ~ 4

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.

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Estimation of protection for COVID-19 in children from epidemiological information and estimate effect of policy in Japan

10.1101/2020.03.27.20045252 ◽

2020 ◽

Author(s):

Junko Kurita ◽

Yoshiyuki Sugishita ◽

Tamie Sugawara ◽

Yasushi Ohkusa

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Contact Pattern ◽

Significant Protection ◽

Age Classes ◽

Protection Level ◽

Number Of Patients ◽

China And Japan ◽

Epidemiological Information ◽

The Basic Reproduction Number

AbstractBackgroundIncidence in children was much less than in adults during the COVID-19 outbreak. Sports and entertainment events were canceled (VEC) in Japan for two weeks during 26 February – 13 March. Most schools were closed (SC).ObjectWe construct a susceptible–infected–recovered model using three age classes and estimate the basic reproduction number (R0) and protection level among children simultaneously. Then we simulate SC and VEC effects.MethodWe used data of patients with symptoms in Japan during 14 January to assess SC and VEC introduction. Effects of SC and VEC were incorporated into the model through change in the contact pattern or frequencies among age classes.ResultsResults suggest R0 as 2.86 [95%CI of 2.73, 2.97]. The protection level was estimated as 0.4 [0.2, 0.7]. SC and VEC can reduce the total number of patients significantly, by 6–7%.Discussion and ConclusionThe estimated R0 was similar to that found from other studies in China and Japan. We found a significant protection level among children, and by effects of SC and VEC. Introduction

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

J ◽

10.3390/j4020008 ◽

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.

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

BMC Research Notes ◽

10.1186/s13104-021-05540-9 ◽

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

Scientific Reports ◽

10.1038/s41598-021-95913-8 ◽

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.

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Persistence in seasonally varying predator–prey systems via the basic reproduction number

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2015.11.007 ◽

2016 ◽

Vol 30 ◽

pp. 73-98 ◽

Cited By ~ 12

Author(s):

Maurizio Garrione ◽

Carlota Rebelo

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Predator Prey ◽

The Basic Reproduction Number

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

Advances in Difference Equations ◽

10.1186/s13662-021-03276-1 ◽

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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