AN EPIDEMIOLOGICAL MODEL WITH MULTIPLE ENDEMIC STATES

2015 ◽  
Vol 23 (supp01) ◽  
pp. S17-S31
Author(s):  
GEISER VILLAVICENCIO-PULIDO ◽  
IGNACIO BARRADAS ◽  
LUNA BEATRIZ
Keyword(s):  
Infectious Disease ◽  
Backward Bifurcation ◽  
Epidemiological Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Force Of Infection

We present a model describing the dynamics of an infectious disease for which the force of infection is diminished through a reaction of the susceptible to the number of infected individuals. We show that, even though the structure of the model is a simple one, different kinds of backward bifurcation can appear for values of the basic reproductive number bigger than one. Under some conditions on the parameters, multiple endemic equilibria may appear for values of the basic reproductive number less or greater than one.

scholarly journals Huanglongbing Model under the Control Strategy of Discontinuous Removal of Infected Trees

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1164
Author(s):  
Weiwei Ling ◽  
Pinxia Wu ◽  
Xiumei Li ◽  
Liangjin Xie
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Control Strategy ◽  
Theoretical Basis ◽  
Dynamic Properties ◽  
Transmission Mechanism ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Vector Borne ◽  
Citrus Trees

By using differential equations with discontinuous right-hand sides, a dynamic model for vector-borne infectious disease under the discontinuous removal of infected trees was established after understanding the transmission mechanism of Huanglongbing (HLB) disease in citrus trees. Through calculation, the basic reproductive number of the model can be attained and the properties of the model are discussed. On this basis, the existence and global stability of the calculated equilibria are verified. Moreover, it was found that different I0 in the control strategy cannot change the dynamic properties of HLB disease. However, the lower the value of I0, the fewer HLB-infected citrus trees, which provides a theoretical basis for controlling HLB disease and reducing expenditure.

scholarly journals An artificially simulated outbreak of a respiratory infectious disease

2020 ◽  
Author(s):  
Zuiyuan Guo ◽  
Shuang Xu ◽  
Libo Tong ◽  
Botao Dai ◽  
Yuandong Liu ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Attack Rate ◽  
General Pattern ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Developmental Trend ◽  
Collision Model ◽  
Military Camp ◽  
Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often occur in crowded places. To understand the pattern of spread of an outbreak of a respiratory infectious disease and provide a theoretical basis for targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 (ADV 7) in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeded 1.5, the median attack rate increased sharply; when R 0 =3, with a delay in the TOI, the attack rate increased gradually and eventually remained stable. When the IOI exceeded 2.3 days, the median attack rate also increased dramatically. When the IR exceeded 0.5, the median attack rate approached zero. The median generation time was 8.26 days, (95% confidence interval [CI]: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusions The random collision model not only simulates how an epidemic spreads with superior precision but also allows greater flexibility in setting the activities of the exposure population and different types of infectious diseases, which is conducive to furthering exploration of the epidemiological characteristics of epidemic outbreaks.

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 An artificially simulated outbreak of a respiratory infectious disease

2020 ◽  
Author(s):  
Zuiyuan Guo ◽  
Shuang Xu ◽  
Libo Tong ◽  
Botao Dai ◽  
Yuandong Liu ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Attack Rate ◽  
General Pattern ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Developmental Trend ◽  
Collision Model ◽  
Military Camp ◽  
Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often occur in crowded places. To understand the pattern of spread of an outbreak of a respiratory infectious disease and provide a theoretical basis for targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 (ADV 7) in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeded 1.5, the median attack rate increased sharply; when R 0 =3, with a delay in the TOI, the attack rate increased gradually and eventually remained stable. When the IOI exceeded 2.3 days, the median attack rate also increased dramatically. When the IR exceeded 0.5, the median attack rate approached zero. The median generation time was 8.26 days, (95% confidence interval [CI]: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusions The random collision model not only simulates how an epidemic spreads with superior precision but also allows greater flexibility in setting the activities of the exposure population and different types of infectious diseases, which is conducive to furthering exploration of the epidemiological characteristics of epidemic outbreaks.

scholarly journals Dynamical Behavior of a New Epidemiological Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zizi Wang ◽  
Zhiming Guo
Keyword(s):  
Time Delay ◽  
Dynamical Behavior ◽  
Endemic Equilibrium ◽  
Epidemiological Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain timeτ. The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive numberR0is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided thatR0≤1; ifR0>1, then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the timeτis also addressed.

scholarly journals Quantifying Uncertainty in Infectious Disease Mechanistic Models

2021 ◽  
Author(s):  
Lucy D’Agostino McGowan ◽  
Kyra H Grantz ◽  
Eleanor Murray
Keyword(s):  
Infectious Disease ◽  
Data Uncertainty ◽  
Basic Reproductive Number ◽  
Sensitivity Analyses ◽  
Reproductive Number ◽  
Mechanistic Models ◽  
Statistical Uncertainty ◽  
Stochastic Uncertainty ◽  
Quantifying Uncertainty

Abstract This primer describes the statistical uncertainty in mechanistic models and provides R code to quantify it. We begin with an overview of mechanistic models for infectious disease, and then describe the sources of statistical uncertainty in the context of a case study on SARS-CoV-2. We describe the statistical uncertainty as belonging to three categories: data uncertainty, stochastic uncertainty, and structural uncertainty. We demonstrate how to account for each of these via statistical uncertainty measures and sensitivity analyses broadly, as well as in a specific case study on estimating the basic reproductive number, ${R}_0$, for SARS-CoV-2.

scholarly journals An artificially simulated outbreak of a respiratory infectious disease

2019 ◽  
Author(s):  
Zuiyuan Guo ◽  
Shuang Xu ◽  
Libo Tong ◽  
Botao Dai ◽  
Yuandong Liu
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Attack Rate ◽  
General Pattern ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Developmental Trend ◽  
Collision Model ◽  
Military Camp ◽  
Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often take place in crowded places. To understand the spreading pattern of an outbreak of a respiratory infectious disease and provide a theoretical basis for the targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between the onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeds 1.5, the median attack rate increases sharply; when R 0 =3, with a delay in the TOI, the attack rate increases gradually and eventually remains stable. If the IOI exceeds 2.3 days, the median attack rate will also increase dramatically. If the IR exceeds 0.5, the median of the attack rate nears zero. The median generation time was 8.26 days (95% CI: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and the R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusion The random collision model not only simulates how an epidemic spreads with superior precision but also allows more flexibility in the settings of the exposure population’s activities and different types of infectious diseases, which is conducive to furthering the exploration of the epidemiological characteristics of epidemic outbreaks.

scholarly journals Adapting an Agent-Based Model of Infectious Disease Spread in an Irish County to COVID-19

Systems ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 41
Author(s):  
Elizabeth Hunter ◽  
John D. Kelleher
Keyword(s):  
Complex System ◽  
Infectious Disease ◽  
Emerging Infectious Diseases ◽  
Disease Outbreaks ◽  
Basic Reproductive Number ◽  
Disease Spread ◽  
Reproductive Number ◽  
Agent Based Model ◽  
School Closures ◽  
Agent Based

The dynamics that lead to the spread of an infectious disease through a population can be characterized as a complex system. One way to model such a system, in order to improve preparedness, and learn more about how an infectious disease, such as COVID-19, might spread through a population, is agent-based epidemiological modelling. When a pandemic is caused by an emerging disease, it takes time to develop a completely new model that captures the complexity of the system. In this paper, we discuss adapting an existing agent-based model for the spread of measles in Ireland to simulate the spread of COVID-19. The model already captures the population structure and commuting patterns of the Irish population, and therefore, once adapted to COVID-19, it can provide important insight on the pandemic, specifically in Ireland. We first investigate the different disease parameters that need to be adjusted to simulate the spread of COVID-19 instead of measles and then run a set of experiments initially comparing the model output for our original measles model with that from the adjusted COVID-19 model. We then report on experiments on how the different values of the basic reproductive number, R0, influence the simulated outbreaks, and find that our model behaves as expected: the higher the R0, the more agents are infected. Then, we demonstrate how different intervention strategies, such as vaccinations and school closures, influence the spread of measles and COVID-19 and how we can simulate real pandemic timings and interventions in our model. We show that with the same society, environment and transportation components among the different disease components lead to very different results for the two diseases, and that our COVID-19 model, when run for Leitrim County, Ireland, predicts a similar outbreak length to a real outbreak in Leitrim County, Ireland, but the model results in a higher number of infected agents compared to the real outbreak. This difference in cases is most likely due to identifying all cases of COVID-19 in the model opposed to only those tested. Once an agent-based model is created to simulate a specific complex system or society, the disease component can be adapted to simulate different infectious disease outbreaks. This makes agent-based models a powerful tool that can be used to help understand the spread of new and emerging infectious diseases.

scholarly journals An artificially simulated outbreak of a respiratory infectious disease

2020 ◽  
Author(s):  
Zuiyuan Guo ◽  
Shuang Xu ◽  
Libo Tong ◽  
Botao Dai ◽  
Yuandong Liu ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Attack Rate ◽  
General Pattern ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Developmental Trend ◽  
Collision Model ◽  
Military Camp ◽  
Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often occur in crowded places. To understand the pattern of spread of an outbreak of a respiratory infectious disease and provide a theoretical basis for targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 (ADV 7) in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeded 1.5, the median attack rate increased sharply; when R 0 =3, with a delay in the TOI, the attack rate increased gradually and eventually remained stable. When the IOI exceeded 2.3 days, the median attack rate also increased dramatically. When the IR exceeded 0.5, the median attack rate approached zero. The median generation time was 8.26 days, (95% confidence interval [CI]: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusions The random collision model not only simulates how an epidemic spreads with superior precision but also allows greater flexibility in setting the activities of the exposure population and different types of infectious diseases, which is conducive to furthering exploration of the epidemiological characteristics of epidemic outbreaks.

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