Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

Li, Tiantian; Xue, Yong

doi:10.4236/am.2013.410a2011

Cited by 21 publications

(13 citation statements)

References 17 publications

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“…SIR/SEIR models have been standard tools used for this purpose [7,8]. SIR/SEIR models including a compartment for quarantined (Q) individuals are called SIQR [10] or SEIQR, respectively [11][12][13]. Some examples of derivatives include the inclusion of isolated patients in the SIR model [11], a delayed SEIQR epidemic model with a vaccination effect [12], or with quarantine and latent compartments [13].…”

Section: Introductionmentioning

confidence: 99%

“…SIR/SEIR models including a compartment for quarantined (Q) individuals are called SIQR [10] or SEIQR, respectively [11][12][13]. Some examples of derivatives include the inclusion of isolated patients in the SIR model [11], a delayed SEIQR epidemic model with a vaccination effect [12], or with quarantine and latent compartments [13]. The outbreak of SARS-CoV-2 has been analyzed by many authors in terms of quarantine rate [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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

Utamura¹,

Koizumi²,

Kirikami³

2020

JMIR Public Health Surveill

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Utamura¹,

Koizumi²,

Kirikami³

2020

JMIR Public Health Surveill

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“…According to Routh-Hurwitz criteria, it is said to be asymptotically local if the eigen value of the real part is negative [11]. By looking for characteristic and qualifying equations:…”

Section: Free Disease Equilibrium Analysismentioning

confidence: 99%

Stability Analysis Model of Plasmodium vivax from Anopheles in Human Infection using SIDR Population Compartment with Treatment RTS-S/AS01 Vaccine in Yogyakarta

Prihantini¹,

Pratama²,

Muhammad³

2017

EJSMT

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As the world population grows, many urban and rural area become the nest of malaria. Malaria is one of the most dangerous diseases for human beings and can be fatal. Malaria is caused by Plasmodium derived from the parasite protozoa class that multiplies in human blood cells. Malaria transmission occurs through the bite of Anopheles female mosquito that has been infected by Plasmodium vivax. The transmission process through the female Anopheles mosquito can be represented in mathematical model with the SIDR population approach. So far, research on mosquito breeding and spread of this type of disease only uses a mathematical model with the SIR population approach. Update from this research is to add populations of dormant species, populations that allow a person to positively heal or not. In this research the quantitative method is used that utilizes history data to create new model to be applied along with treatment that determined the RTS-S/AS01 vaccine does influence to prevention and reduction of infected population. The results obtained based on the model and graph is the treatment of RTS-S/AS01 vaccine which can reduce the number of infected population. Therefore, it can be concluded that the RTS-S/AS01 vaccine can prevent the spread of malaria disease. The objective of this study is to examine the spread of malaria and provide the solutions that malaria can be prevented from spreading using the RTS-S/AS01 vaccine.

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“…Models with a compartment for quarantined individuals are called SIQR model [5] or SEIQR model [6], [7], [8]. The occurrence of the transition from the component I to Q, which is observed as a number of newly found infected patients, is usually assumed to be proportional to the number of infectious patients at large, and this proportionality coefficient is treated as a parameter called "quarantine rate".…”

Section: Introductionmentioning

confidence: 99%

A delayed SEIQR epidemic model of COVID-19 in Tokyo

Maki¹

2020

Preprint

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The rapid expansion of COVID-19 has caused a global pandemic. In order to avoid excessive restriction to the social activity, a good strategy of quarantine is needed. Several epidemic models with a quarantine compartment such as susceptible-exposed-infectious-quarantined-removed (SEIQR) model have been applied. However, in the actual situation, the infection test and quarantine is often delayed from the beginning of the infectious stage. This article presents a delayed SEIQR model to analyze the effect of the delay of quarantine, and to suggest a guideline for the measure. The latency period (compartment E) was assumed to be 3 days, and the start of quarantine action was assumed to be delayed by 4 to 10 days from infection. The actual PCR test-positive number data from March 10th to July 18th in 2020 was analyzed to estimate a transmission rate and the reproduction number. The area where the infection expansion is restrained was displayed in the two parameter space (transmission rate and quarantine rate) for several possible lengths of the delay of quarantine. As a result, it was shown to be very hard to restrain the expansion of infection only by a simple quarantine action retaining the delay. As a short term measure, it was found to be necessary to reduce the transmission rate through some kind of restriction of social activity, but as a long term measure, it was found to be possible to maintain the social activity by shortening the delay of quarantine through expanding the infection test system to find earlier stage patients, including asymptomatic infectious patients. In order to shed light to this conclusion from a different viewpoint, this model was applied in another case that an additional quarantine was taken into account before the delay. The result was shown to have a similar effect as that of the shortening of the delay.

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Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

Cited by 21 publications

References 17 publications

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

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

Stability Analysis Model of Plasmodium vivax from Anopheles in Human Infection using SIDR Population Compartment with Treatment RTS-S/AS01 Vaccine in Yogyakarta

A delayed SEIQR epidemic model of COVID-19 in Tokyo

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