scholarly journals Epidemic spreading model in heterogeneous conditions

2021 ◽  
pp. 1-12
Author(s):  
Andrey Viktorovich Podlazov
Keyword(s):  
Equilibrium Position ◽  
Sir Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Epidemic Spread ◽  
Epidemic Spreading ◽  
Oscillatory Dynamics ◽  
Spreading Model ◽  
Multiple Contacts ◽  
The Social

I propose two modifications of the SIR model of the epidemic spread, taking into account the social and space heterogeneity of the population. Social hetero¬geneity associated with differences in the intensity of paired contacts between people qualitatively changes the basic reproductive number. Space heterogeneity associated with differences in the intensity of multiple contacts between people significantly shifts the equilibrium position, increases the characteristic times and leads to the emergence of oscillatory dynamics of finite duration.

DYNAMICS OF EPIDEMIC SPREADING MODEL WITH DISTRIBUTED DELAY ON HETEROGENEOUS NETWORK

2017 ◽  
Vol 25 (01) ◽  
pp. 173-183 ◽  
Author(s):  
QIMING LIU ◽  
MEICI SUN
Keyword(s):  
Heterogeneous Network ◽  
Distributed Delay ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Epidemic Spreading ◽  
Spreading Model

A novel [Formula: see text] epidemic spreading model with distributed delay on complex heterogeneous network is presented. The formula of the basic reproductive number is presented to the model. It is proven that the disease dies out if the basic reproductive number is less than unity, while if the basic reproductive number is more than unity, the disease is uniformly persistent. The results enrich the previous results.

scholarly journals Dynamics analysis of an online gambling spreading model on scale-free networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yu Kong ◽  
Tao Li ◽  
Yuanmei Wang ◽  
Xinming Cheng ◽  
He Wang ◽  
...  
Keyword(s):  
Network Topology ◽  
Negative Impact ◽  
Online Gambling ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Scale Free ◽  
Spreading Model ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
Gambling Policy

AbstractNowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new SHGD (susceptible–hesitator–gambler–disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive number $R_{0}$ R 0 is got and analyzed. The basic reproductive number $R_{0}$ R 0 is related to anti-gambling policy and the network topology. Then, gambling-free equilibrium $E_{0}$ E 0 and gambling-prevailing equilibrium $E_{ +} $ E + are obtained. The global stability of $E_{0}$ E 0 is analyzed. The global attractivity of $E_{ +} $ E + and the persistence of online gambling phenomenon are studied. Finally, the theoretical results are verified by some simulations.

SE2IR Invest Market Rumor Spreading Model Considering Hesitating Mechanism

2019 ◽  
Vol 7 (1) ◽  
pp. 54-69 ◽  
Author(s):  
Hongxing Yao ◽  
Xiangyang Gao
Keyword(s):  
Mean Field ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Field Equations ◽  
Rumor Spreading ◽  
Immunization Strategy ◽  
Scale Free ◽  
Spreading Model ◽  
Mean Field Equations ◽  
The Impact

Abstract According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-field equations is obtained on scale-free network. In this paper, we first combine the theory of spreading dynamics and find out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the final rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions: Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.

scholarly journals Estimation of the Basic Reproduction Number of Novel Influenza A (H1N1) pdm09 in Elementary Schools Using the SIR Model

2017 ◽  
Vol 11 (1) ◽  
pp. 64-72 ◽  
Author(s):  
Daisuke Furushima ◽  
Shoko Kawano ◽  
Yuko Ohno ◽  
Masayuki Kakehashi
Keyword(s):  
Elementary Schools ◽  
Infection Rate ◽  
School Size ◽  
Influenza A ◽  
Missing Values ◽  
Sir Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Influenza A H1n1 ◽  
Novel Influenza A

Background: The novel influenza A (H1N1) pdm09 (A/H1N1pdm) pandemic of 2009-2010 had a great impact on society. Objective: We analyzed data from the absentee survey, conducted in elementary schools of Oita City, to evaluate the A/H1N1pdm pandemic and to estimate the basic reproductive number (R0 ) of this novel strain. Method: We summarized the overall absentee data and calculated the cumulative infection rate. Then, we classified the data into 3 groups according to school size: small (<300 students), medium (300–600 students), and large (>600 students). Last, we estimated the R0 value by using the Susceptible-Infected-Recovered (SIR) mathematical model. Results: Data from 60 schools and 27,403 students were analyzed. The overall cumulative infection rate was 44.4%. There were no significant differences among the grades, but the cumulative infection rate increased as the school size increased, being 37.7%, 44.4%, and 46.6% in the small, medium, and large school groups, respectively. The optimal R0 value was 1.33, comparable with that previously reported. The data from the absentee survey were reliable, with no missing values. Hence, the R0 derived from the SIR model closely reflected the observed R0 . The findings support previous reports that school children are most susceptible to A/H1N1pdm virus infection and suggest that the scale of an outbreak is associated with the size of the school. Conclusion: Our results provide further information about the A/H1N1pdm pandemic. We propose that an absentee survey should be implemented in the early stages of an epidemic, to prevent a pandemic.

scholarly journals An Epidemiological Model Considering Isolation to Predict COVID-19 Trends in Tokyo, Japan: Numerical Analysis (Preprint)

2020 ◽  
Author(s):  
Motoaki Utamura ◽  
Makoto Koizumi ◽  
Seiichi Kirikami
Keyword(s):  
Public Health ◽  
Transmission Rate ◽  
Time Lag ◽  
Sir Model ◽  
Epidemiological Model ◽  
Basic Reproductive Number ◽  
Polymerase Chain Reaction Test ◽  
Series Data ◽  
Reproductive Number ◽  
Alternative Formulation

BACKGROUND COVID-19 currently poses a global public health threat. Although Tokyo, Japan, is no exception to this, it was initially affected by only a small-level epidemic. Nevertheless, medical collapse nearly happened since no predictive methods were available to assess infection counts. A standard susceptible-infectious-removed (SIR) epidemiological model has been widely used, but its applicability is limited often to the early phase of an epidemic in the case of a large collective population. A full numerical simulation of the entire period from beginning until end would be helpful for understanding COVID-19 trends in (separate) counts of inpatient and infectious cases and can also aid the preparation of hospital beds and development of quarantine strategies. OBJECTIVE This study aimed to develop an epidemiological model that considers the isolation period to simulate a comprehensive trend of the initial epidemic in Tokyo that yields separate counts of inpatient and infectious cases. It was also intended to induce important corollaries of governing equations (ie, effective reproductive number) and equations for the final count. METHODS Time-series data related to SARS-CoV-2 from February 28 to May 23, 2020, from Tokyo and antibody testing conducted by the Japanese government were adopted for this study. A novel epidemiological model based on a discrete delay differential equation (apparent time-lag model [ATLM]) was introduced. The model can predict trends in inpatient and infectious cases in the field. Various data such as daily new confirmed cases, cumulative infections, inpatients, and PCR (polymerase chain reaction) test positivity ratios were used to verify the model. This approach also derived an alternative formulation equivalent to the standard SIR model. RESULTS In a typical parameter setting, the present ATLM provided 20% less infectious cases in the field compared to the standard SIR model prediction owing to isolation. The basic reproductive number was inferred as 2.30 under the condition that the time lag <i>T</i> from infection to detection and isolation is 14 days. Based on this, an adequate vaccine ratio to avoid an outbreak was evaluated for 57% of the population. We assessed the date (May 23) that the government declared a rescission of the state of emergency. Taking into consideration the number of infectious cases in the field, a date of 1 week later (May 30) would have been most effective. Furthermore, simulation results with a shorter time lag of <i>T</i>=7 and a larger transmission rate of α=1.43α0 suggest that infections at large should reduce by half and inpatient numbers should be similar to those of the first wave of COVID-19. CONCLUSIONS A novel mathematical model was proposed and examined using SARS-CoV-2 data for Tokyo. The simulation agreed with data from the beginning of the pandemic. Shortening the period from infection to hospitalization is effective against outbreaks without rigorous public health interventions and control.

scholarly journals MEASUREMENT AND INTERNALIZATION OF SYSTEMIC RISK IN A GLOBAL BANKING NETWORK

2013 ◽  
Vol 24 (01) ◽  
pp. 1250093 ◽  
Author(s):  
XIAOBING FENG ◽  
HAIBO HU
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Systemic Risk ◽  
Bank Failure ◽  
Bank Failures ◽  
Negative Externalities ◽  
Epidemic Spreading ◽  
Spreading Model ◽  
The Social ◽  
Global Banking

The negative externalities from an individual bank failure to the whole system can be huge. One of the key purposes of bank regulation is to internalize the social costs of potential bank failures via capital charges. This study proposes a method to evaluate and allocate the systemic risk to different countries/regions using a Susceptible-Infected-Removable (SIR) type of epidemic spreading model and the Shapley value (SV) in game theory. The paper also explores features of a constructed bank network using real globe-wide banking data.

scholarly journals Dynamics Analysis of a Betel Nut Addiction Spreading Model on Scale-Free Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
He Wang ◽  
Tao Li ◽  
Xinming Cheng ◽  
Yu Kong ◽  
Yangmei Lei
Keyword(s):  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Betel Nut ◽  
Globally Asymptotically Stable ◽  
Scale Free ◽  
Face To Face ◽  
Spreading Model ◽  
Scale Free Networks ◽  
Globally Attractive ◽  
Existence Of Equilibria

Medical research has shown that overeating betel nut can be addictive and can damage health. More serious cases may cause mouth cancer and other diseases. Even worse, people’s behavior habit of chewing betel nut may influence each other through social interaction with direct or indirect ways, such as face-to-face communication, Facebook, Twitter, microblog, and WeChat, which leads to the spreading phenomenon of betel nut addiction. In order to investigate the dynamic spreading characteristics of betel nut addiction, a PMSR (Potential-Mild-Severe-Recovered) betel nut addiction spreading model is presented on scale-free networks. The basic reproductive number R0 and equilibria are derived. Theoretical results indicate that the basic reproductive number R0 is significantly dependent on the topology of the underlying networks, and some influence parameters. The existence of equilibria is determined by the basic reproductive number R0. Furthermore, we prove that if R0<1 the addiction-elimination equilibrium is globally asymptotically stable. If R0>1, the betel nut addiction spreading is permanent, and the addiction-prevailing equilibrium is globally attractive. Finally, numerical simulations confirm the theoretical analysis results.

scholarly journals Solvable delay model for epidemic spreading: the case of Covid-19 in Italy

2020 ◽  
Author(s):  
Luca Dell’Anna
Keyword(s):  
Large Population ◽  
Realistic Model ◽  
Sir Model ◽  
Delay Model ◽  
Epidemic Spreading ◽  
The Social ◽  
Containment Measures ◽  
The Government ◽  
Functional Delay ◽  
Delay Differential

We present a simple but realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of a set of three ordinary differential equations. We apply our model to describe the outbreak of the new virus COVID-19 in Italy, taking into account the containment measures implemented by the government in order to mitigate the spreading of the virus and the social costs for the population.

scholarly journals An Epidemiological Model Considering Isolation to Predict COVID-19 Trends in Tokyo, Japan: Numerical Analysis

10.2196/23624 ◽  
2020 ◽  
Vol 6 (4) ◽  
pp. e23624
Author(s):  
Motoaki Utamura ◽  
Makoto Koizumi ◽  
Seiichi Kirikami
Keyword(s):  
Public Health ◽  
Transmission Rate ◽  
Time Lag ◽  
Sir Model ◽  
Epidemiological Model ◽  
Basic Reproductive Number ◽  
Polymerase Chain Reaction Test ◽  
Series Data ◽  
Reproductive Number ◽  
Alternative Formulation

Background COVID-19 currently poses a global public health threat. Although Tokyo, Japan, is no exception to this, it was initially affected by only a small-level epidemic. Nevertheless, medical collapse nearly happened since no predictive methods were available to assess infection counts. A standard susceptible-infectious-removed (SIR) epidemiological model has been widely used, but its applicability is limited often to the early phase of an epidemic in the case of a large collective population. A full numerical simulation of the entire period from beginning until end would be helpful for understanding COVID-19 trends in (separate) counts of inpatient and infectious cases and can also aid the preparation of hospital beds and development of quarantine strategies. Objective This study aimed to develop an epidemiological model that considers the isolation period to simulate a comprehensive trend of the initial epidemic in Tokyo that yields separate counts of inpatient and infectious cases. It was also intended to induce important corollaries of governing equations (ie, effective reproductive number) and equations for the final count. Methods Time-series data related to SARS-CoV-2 from February 28 to May 23, 2020, from Tokyo and antibody testing conducted by the Japanese government were adopted for this study. A novel epidemiological model based on a discrete delay differential equation (apparent time-lag model [ATLM]) was introduced. The model can predict trends in inpatient and infectious cases in the field. Various data such as daily new confirmed cases, cumulative infections, inpatients, and PCR (polymerase chain reaction) test positivity ratios were used to verify the model. This approach also derived an alternative formulation equivalent to the standard SIR model. Results In a typical parameter setting, the present ATLM provided 20% less infectious cases in the field compared to the standard SIR model prediction owing to isolation. The basic reproductive number was inferred as 2.30 under the condition that the time lag T from infection to detection and isolation is 14 days. Based on this, an adequate vaccine ratio to avoid an outbreak was evaluated for 57% of the population. We assessed the date (May 23) that the government declared a rescission of the state of emergency. Taking into consideration the number of infectious cases in the field, a date of 1 week later (May 30) would have been most effective. Furthermore, simulation results with a shorter time lag of T=7 and a larger transmission rate of α=1.43α0 suggest that infections at large should reduce by half and inpatient numbers should be similar to those of the first wave of COVID-19. Conclusions A novel mathematical model was proposed and examined using SARS-CoV-2 data for Tokyo. The simulation agreed with data from the beginning of the pandemic. Shortening the period from infection to hospitalization is effective against outbreaks without rigorous public health interventions and control.

Spreading Dynamics Analysis of a Novel SEAIRS Epidemic Model with Protection and Hospital Quarantine under Government Pre-warning

2021 ◽  
Author(s):  
Bingchuan Xue ◽  
Tao Li ◽  
Xinming Cheng ◽  
Yumiao Li ◽  
Yuanyuan Wu ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Spreading Dynamics ◽  
The Mean ◽  
The Impact

Abstract To study the impact of protection and hospital quarantine measure, government pre-warning mechanism and heterogeneity of underlying networks on epidemic spreading, a novel SEAIRS epidemic model is proposed on scale-free networks. The spreading dynamics of the model is studied by means of the mean-field theory. Two equilibriums and the basic reproductive number R0 of the model is analyzed in detail. The global asymptotic stability of the disease-free equilibrium, the permanence of the epidemic spreading and the global attractivity of the endemic equilibrium are proved. Sensitivity analysis shows that the basic reproductive number R0 is dependent on the coverage rate of home quarantine (ωQ,ηA ,ηS ), hospitalization rate η1 and government pre-warning intensity δ . Finally, the theoretical analysis results are confirmed by means of numerical simulations.

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