Simple Forward Finite Difference for Computing Reproduction Number of COVID-19 in Indonesia During the New Normal

The research purpose shown in this article is describing the time dependent reproduction number of coronavirus called by COVID-19 in the new normal period for 3 types areas, i.e. small, medium and global areas by considering the number of people in these areas. It is known that in early June 2020, Indonesia has claimed to open activities during the pandemic with the new normal system. Though the number of COVID-19 cases is still increasing in almost infected areas, normal activities are coming back with healty care protocols where public areas are opened as usual with certain restrictions. In order to have observations of spreading impact of COVID-19, the basic reproduction number (Ro) i.e. the reproduction number (Ro) is the ratio between 2 parameters of SIR model where SIR stands for Susceptible individuals, Infected individuals, and Recovered individuals respectively. The reproduction numbers are computed as discrete values depending on time. The used research method is finite difference scheme for computing rate of change parameters in SIR models based on the COVID-19 cases in Indonesia (global area), Jakarta (medium area) and Salatiga (small area) by considering the number of people in these areas respectively. The simple forward finite difference is employed to the SIR model to have time dependent of parameters. The second approach is using the governing linear system to obtain the values of parameter daily. These parameters are computed for each day such that the values of Ro are obtained as function of time. The research result shows that 3 types areas give the same profiles of parameters that the rate of changes of reproduction numbers are decreasing with respect to time. This concludes that the reproduction numbers are most likely decreasing.

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COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

10.2196/preprints.23997 ◽

2020 ◽

Author(s):

Eduardo Atem De Carvalho ◽

Rogerio Atem De Carvalho

Keyword(s):

New York ◽

Reproduction Number ◽

Moving Average ◽

Real Data ◽

Time Dependent ◽

Initial Value ◽

Health Authorities ◽

Reproduction Numbers ◽

Effect Estimation ◽

The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

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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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Estimation of the Time-dependent Reproduction Number of Influenza A(H1N1)pdm2009 in South Korea

10.21203/rs.3.rs-20387/v1 ◽

2020 ◽

Author(s):

Yunjeong Lee ◽

Dong Han Lee ◽

Hee-Dae Kwon ◽

Changsoo Kim ◽

Jeehyun Lee

Keyword(s):

South Korea ◽

Influenza A ◽

Reproduction Number ◽

Time Estimation ◽

Time Dependent ◽

Estimation Of Parameters ◽

Transmission Potential ◽

Reproduction Numbers ◽

Influenza A H1n1 ◽

Feasible Range

Abstract Background: The reproduction number is one of the most crucial parameters in determining disease dynamics, providing a summary measure of the transmission potential. However, estimating this value is particularly challenging owing to the characteristics of epidemic data, including non-reproducibility and incompleteness.Methods: In this study, we propose mathematical models with different population structures; each of these models can produce data on the number of cases of the influenza A(H1N1)pdm09 epidemic in South Korea. These structured models incorporating the heterogeneity of age and region are used to estimate the time-dependent effective reproduction numbers. Subsequently, the age- and region-specific reproduction numbers are also computed to analyze the differences illustrated in the incidence data.Results: The basic SIR fails to provide a reasonable estimation of the reproduction numbers. The estimated values demonstrate a large variation and remains outside of the feasible range for the influenza, regardless of the time period for data. Real-time estimation using age- and region-structured models demonstrated that the effective reproduction number rose sharply during mid-October when the ㅜumber of patients increased dramatically. The reproduction number fell below unity at the end of October and stayed lower than unity indicating that the epidemic starts decreasing, which is consistent with the incidence data.Conclusions: Numerical results reveal that the introduction of heterogeneity into the population to represent the general characteristics of dynamics is essential for the robust estimation of parameters.

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Basic and effective reproduction numbers of COVID-19 cases in South Korea excluding Sincheonji cases

10.1101/2020.03.19.20039347 ◽

2020 ◽

Cited By ~ 7

Author(s):

Jeongeun Hwang ◽

Hyunjung Park ◽

Jiwon Jung ◽

Sung-Han Kim ◽

Namkug Kim

Keyword(s):

South Korea ◽

Basic Reproduction Number ◽

Infection Prevention ◽

Reproduction Number ◽

Hand Washing ◽

Time Dependent ◽

Government Policies ◽

Black Swan ◽

Reproduction Numbers ◽

Near Future

AbstractIn February and March 2020, COVID-19 epidemic in South Korea met a large black swan effect by a Sincheonji cult mass infection in Daegu-Gyeongbuk area. The black swan made it difficult to evaluate that the current policies for infection prevention including social distancing, closing schools, hand washing, and wearing masks good enough or not. Therefore, in this study, we evaluated basic reproduction number (R0) and time-dependent reproduction number (Rt) of confirmed cases based on various kinds of populations, including total, Daegu-Geyoengbuk, except-Daegu-Gyeongbuk, Sincheonji, and except-Sincheonji. In total, it seems the infection is going to be under control, but this is never true because in the except-Sincheonji and except-Daegu-Geyongbuk cases, R0 is still above 1.0, and Rt is drifting around 1.0. This study could be used to determine government policies in the near future.

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What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?

10.1101/2021.06.16.21259019 ◽

2021 ◽

Author(s):

quentin Griette ◽

Jacques Demongeot ◽

pierre magal

Keyword(s):

Social Interactions ◽

Reproduction Number ◽

Transmission Rate ◽

Social Effects ◽

Time Dependent ◽

Reproduction Numbers ◽

The Social ◽

The World ◽

Early Beginning ◽

Case Data

Background: The COVID-19 epidemic, which started in late December 2019 and rapidly spread throughout the world, was accompanied by an unprecedented release of reported case data. Our objective is to propose a fresh look at this data by coupling a phenomenological description to the epidemiological dynamics. Methods: We use a phenomenological model to describe and regularize the data. This model can be matched by a single mathematical model reproducing the epidemiological dynamics with a time-dependent transmission rate. We provide a method to compute this transmission rate and reconstruct the changes in the social interactions between people as well as changes in host-pathogen interactions. This method is applied to the cumulative case data of 8 different geographic areas. Findings: We reconstruct the transmission rate from the data, therefore we are in position to understand the contribution of the dynamical effects of social interactions (contacts between individuals) and the contribution of the dynamics of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important in the dynamic of COVID-19. We obtain an instantaneous reproduction number that stays below $3.5$ from early beginning of the epidemic. Conclusion: The instantaneous reproduction number staying below $3.5$ implies that it is sufficient to vaccinate $71\%$ of the population in each state or country considered in our study. Therefore assuming the vaccines will remain efficient against the new variants, and to be more confident it is sufficient to vaccinate $75-80\%$ to get rid of COVID-19 in each state or country. Funding: This research was funded by the Agence Nationale de la Recherche in France (Project name: MPCUII (PM) and (QG))

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kifli PENERAPAN METODE RESITASI DI MASA NEW NORMAL PADA MATA PELAJARAN IPS KELAS V DI SDN INPRES PAKOWA KABUPATEN BANGGAI

IBTIDAI'Y DATOKARAMA: JURNAL PENDIDIKAN DASAR ◽

10.24239/ibtidaiy.vol2.iss1.25 ◽

2021 ◽

Vol 2 (1) ◽

pp. 37-50

Author(s):

Kifli Bonenehu ◽

Karmawati Karmawati ◽

Rahmawaty Rahmawaty

Keyword(s):

Social Studies ◽

Learning Process ◽

Research Result ◽

Application Process ◽

Class V ◽

New Normal ◽

Main Research ◽

Assignment Method ◽

Inhibiting Factors ◽

Normal Period

This thesis discusses "Application of the Recitation Method in the New Normal Period in Social Studies Subject Class V SDN Inpres Pakowa Banggai Regency. The main research problems are the application process of the recitation method in social studies subjects for a fifth-grade student at SDN Inpres Pakowa Banggai Regency during the new-normal period. Together with factors that hinder the implementation recitation method in social studies subjects class V SDN Inpres Pakowa Banggai Regency in the "new normal" period. The purpose of this study was to determine the application of the recitation method to social studies subjects for class V at SDN Inpres Pakowa, Banggai Regency during the new-normal period and to find out the inhibiting factors for implementing the recitation method in the new-normal period in social studies subjects for class V at SDN Inpres Pakowa, Banggai Regency. This type of research uses qualitative research by describing information data based on facts (facts) obtained in the field. Data collection techniques in this study used observation, interviews, and documentation techniques to describe the learning process at SDN Inpres Pakowa, Banggai Regency during the new-normal period, especially in class V at SDN Inpres Pakowa. The research result shows that SDN Inpres Pakowa applies one of the learning methods to assist the continuity of learning, namely the recitation method or what is known as the assignment method. The learning process was implemented offline at SDN Inpres Pakowa during the new-normal period. The application of the recitation method was carried out by dividing two groups into one class consisting of 14 people divided into 7th people per group. There are inhibiting factors in the new-normal period, namely learning inhibiting factors, lack of learning resources, and weaknesses in applying the recitation method.

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Modifikasi Model SIR pada Penyebaran Penyakit Demam Berdarah Dengue di Kabupaten Bone

Journal of Mathematics, Computations, and Statistics ◽

10.35580/jmathcos.v1i2.9240 ◽

2019 ◽

Vol 1 (2) ◽

pp. 169

Author(s):

Syafruddin Side ◽

A Alimuddin ◽

Alvioni Bani

Keyword(s):

Dengue Fever ◽

Basic Reproduction Number ◽

Epidemic Model ◽

Reproduction Number ◽

Equilibrium Points ◽

Sir Model ◽

District Health Office ◽

District Health ◽

Reproduction Numbers

Abstrak. Artikel ini membahas mengenai modifikasi model epidemik SIR pada penyebaran penyakit DBD di Kabupaten Bone dengan penembahan asumsi baru bahwa 20% penderita DBD yang sembuh akan kembali terinfeksi dan 80 % dari individu yang telah sembuh, tidak akan kembali menjadi rentan. Data yang digunakan adalah jumlah penderita DBD di Kabupaten Bone tahun 2016 dari Dinas Kesehatan Kabupaten Bone. Pembahasan dimulai dari penentuan titik equilibrium, stabilitas, bilangan reproduksi dasar dan simulasi menggunakan Maple. Dalam penelitian ini diperoleh dua titik equilibrium dengan nilai reproduksi dasar . Hal ini menunjukkan bahwa penyakit DBD di Kabupaten Bone akan terus meningkat dan menjadi endemik.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, DBD, Modifikasi Model SIR. Abstract. The research discusses a modification of epidemic model SIR on the spreadof dengue fever disease in Bone District. With some addition of the assumption that 20% of patients who recovered will be re-infected and 80% of individuals who have recovered will not be susceptible. The data used in the number of dengue fever patients in Bone District in 2016 from Bone District Health Office. The discussion starts by the determination of equilibrium points, stability and basic reproduction numbers . In this study, we obtained that two equilibrium points and basic reproduktion value . This indicates that dengue fever disease in Bone District will increase and become endemic.Keywords: Equilibrium Point, Basic Reproduction Number, Dengue Fever, The Modification of SIR Model.

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What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2022025 ◽

2021 ◽

Vol 19 (1) ◽

pp. 537-594

Author(s):

Quentin Griette ◽

◽

Jacques Demongeot ◽

Pierre Magal ◽

Keyword(s):

Social Interactions ◽

Phenomenological Model ◽

Epidemic Model ◽

Reproduction Number ◽

Transmission Rate ◽

Time Dependent ◽

Wave Dynamics ◽

Dependent Rate ◽

Reproduction Numbers ◽

The One

<abstract><p>The COVID-19 outbreak, which started in late December 2019 and rapidly spread around the world, has been accompanied by an unprecedented release of data on reported cases. Our objective is to offer a fresh look at these data by coupling a phenomenological description to the epidemiological dynamics. We use a phenomenological model to describe and regularize the reported cases data. This phenomenological model is combined with an epidemic model having a time-dependent transmission rate. The time-dependent rate of transmission involves changes in social interactions between people as well as changes in host-pathogen interactions. Our method is applied to cumulative data of reported cases for eight different geographic areas. In the eight geographic areas considered, successive epidemic waves are matched with a phenomenological model and are connected to each other. We find a single epidemic model that coincides with the best fit to the data of the phenomenological model. By reconstructing the transmission rate from the data, we can understand the contributions of the changes in social interactions (contacts between individuals) on the one hand and the contributions of the epidemiological dynamics on the other hand. Our study provides a new method to compute the instantaneous reproduction number that turns out to stay below $ 3.5 $ from the early beginning of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important factor in understanding the epidemic wave dynamics for COVID-19. The instantaneous reproduction number stays below $ 3.5 $, which implies that it is sufficient to vaccinate $ 71\% $ of the population in each state or country considered in our study. Therefore, assuming the vaccines will remain efficient against the new variants and adjusting for higher confidence, it is sufficient to vaccinate $ 75-80\% $ to eliminate COVID-19 in each state or country.</p></abstract>

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Model Matematika SIR Sebagai Solusi Kecanduan Penggunaan Media Sosial

Journal of Mathematics, Computations, and Statistics ◽

10.35580/jmathcos.v3i2.20124 ◽

2020 ◽

Vol 3 (2) ◽

pp. 126

Author(s):

Syafruddin Side ◽

Wahidah Sanusi ◽

Nur Khaerati Rustan

Keyword(s):

Social Media ◽

Reproduction Number ◽

Equilibrium Points ◽

Sir Model ◽

Primary Data ◽

Type Model ◽

Social Media Addiction ◽

Reproduction Numbers ◽

Simulation Results ◽

Use Of Social Media

Penelitian ini bertujuan untuk membangun model SIR (Susceptible – Infected – Recovered) sebagai solusi kecanduan penggunaan media sosial dengan asumsi bahwa mahasiswa yang sembuh dari kecanduan media sosial karena memiliki kontrol diri tinggi. Model ini dibagi menjadi tiga kelas yaitu kelas mahasiswa yang berpotensi menggunakan media sosial, kelas mahasiswa yang kecanduan media sosial, dan kelas mahasiswa yang memiliki kontrol diri tinggi. Data yang digunakan adalah data primer yang diperoleh dengan membagikan kuesioner kepada 145 mahasiswa Jurusan Matematika FMIPA UNM angkatan 2017, 2018, dan 2019. Hasil data riil model tipe SIR menghasilkan bilangan reproduksi dasar (R0) sebesar yang berarti bahwa jumlah mahasiswa yang kecanduan penggunaan media sosial akan meningkat dalam kurun waktu tertentu.Kata Kunci: Titik Ekuilibrium, Bilangan Reproduksi Dasar, Media Sosial, Kontrol Diri, Model SIRThis study aims to build the SIR (Susceptible - Infected - Recovered) model as a solution of social media addiction with the assumption that students who recover from addiction of social media because they have high selfcontrol. This model is divided into three classes: namely class of students who have potential to use social media, class of students who are addicted to social media, and class of students who have high selfcontrol. The data used are primary data that was obtained by distributing questionnaires to 145 students of mathematics departement FMIPA UNM class of 2017, 2018, and 2019. The simulation results of the SIR type model produce a basic reproduction number (R0) of 1.451136 which means that the number of students who are addicted to the use of social media will increase in a certain period of time.Keywords: Equilibrium Points, Basic Reproduction Numbers, Social Media, Selfcontrol, SIR Model

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COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling

10.1101/2020.07.28.20164087 ◽

2020 ◽

Author(s):

Eduardo Atem De Carvalho ◽

Rogerio Atem De Carvalho

Keyword(s):

New York ◽

Reproduction Number ◽

Moving Average ◽

Real Data ◽

Time Dependent ◽

Initial Value ◽

Health Authorities ◽

Reproduction Numbers ◽

Effect Estimation ◽

The Impact

Background: Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. Objective: This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. Methods: The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. Results: Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. Conclusions: We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent Reproduction Numbers (Rt), as well as we demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

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