Susceptible-Exposed-Infective-Recovered Research Articles

Predict The Spread of COVID-19 in Iran with A SEIR Model

The current coronavirus disease 2019 (COVID-19) outbreak has recently been declared a pandemic and spread over 200 countries and territories. Forecasting the long-term trend of the COVID-19 epidemic can help health authorities determine the transmission characteristics of the virus and take appropriate prevention and control strategies beforehand. Previous studies that solely applied traditional epidemic models or machine learning models were subject to underfitting or overfitting problems. This paper designed a predictive model based on the mathematical model Susceptible-Exposed-Infective-Recovered (SEIR). SEIR is represented by a set of differential-algebraic equations incorporated with machine learning techniques to fit the data reported to estimate the spread of the COVID-19 epidemic in long-term in the Islamic Republic of Iran up to the end of July 0f 2020. This paper reduced R0 after a certain amount of days to account for containment measures and used delays to allow for lagging official data. Two evaluation criteria, R2 and RMSE, had used in this research which estimates the model on officially reported confirmed cases from different regions in Iran. The results proved the model’s effectiveness in simulating and predicting the trend of the COVID-19 outbreak. Results showed the integrated approach of epidemic and machine learning models could accurately forecast the long-term trend of the COVID-19 outbreak.

Computational simulation of the COVID-19 epidemic with the SEIR stochastic model.

A small number of individuals infected within a community can lead to the rapid spread of the disease throughout that community, leading to an epidemic outbreak. This is even more true for highly contagious diseases such as COVID-19, known to be caused by the new coronavirus SARS-CoV-2. Mathematical models of epidemics allow estimating several impacts on the population and, therefore, are of great use for the definition of public health policies. Some of these measures include the isolation of the infected (also known as quarantine), and the vaccination of the susceptible. In a possible scenario in which a vaccine is available, but with limited access, it is necessary to quantify the levels of vaccination to be applied, taking into account the continued application of preventive measures. This work concerns the simulation of the spread of the COVID-19 disease in a community by applying the Monte Carlo method to a Susceptible-Exposed-Infective-Recovered (SEIR) stochastic epidemic model. To handle the computational effort involved, a simple parallelization approach was adopted and deployed in a small HPC cluster. The developed computational method allows to realistically simulate the spread of COVID-19 in a medium-sized community and to study the effect of preventive measures such as quarantine and vaccination. The results show that an effective combination of vaccination with quarantine can prevent the appearance of major epidemic outbreaks, even if the critical vaccination coverage is not reached.

Retrospect: The Outbreak Evaluation of COVID-19 in Wuhan District of China.

There were 27 novel coronavirus pneumonia cases found in Wuhan, China in December 2019, named as 2019-nCoV temporarily and COVID-19 formally by the World Health Organization (WHO) on the 11 February 2020. In December 2019 and January 2020, COVID-19 has spread on a large scale among the population, which brought terrible disaster to the life and property of the Chinese people. In this paper, we analyze the features and pattern of the virus transmission. Considering the influence of indirect transmission, a conscious-based Susceptible-Exposed-Infective-Recovered (SEIR) (C-SEIR) model is proposed, and the difference equation is used to establish the model. We simulated the C-SEIR model and key important parameters. The results show that (1) increasing people’s awareness of the virus can effectively reduce the spread of the virus; (2) as the capability and possibility of indirect infection increases, the proportion of people being infected will also increase; (3) the increased cure rate can effectively reduce the number of infected people. Then, the virus transmission can be modelled and used for the inflexion and extinction period of pandemic development so as to provide theoretical support for the Chinese government in the decision-making of pandemic prevention and recovery of economic production. Further, this study has demonstrated the effectiveness of the prevention measures taken by the Chinese government such as multi-level administrative district isolation and public health awareness.

Forecasting the long-term trend of COVID-19 epidemic using a dynamic model

The current outbreak of coronavirus disease 2019 (COVID-19) has recently been declared as a pandemic and spread over 200 countries and territories. Forecasting the long-term trend of the COVID-19 epidemic can help health authorities determine the transmission characteristics of the virus and take appropriate prevention and control strategies beforehand. Previous studies that solely applied traditional epidemic models or machine learning models were subject to underfitting or overfitting problems. We propose a new model named Dynamic-Susceptible-Exposed-Infective-Quarantined (D-SEIQ), by making appropriate modifications of the Susceptible-Exposed-Infective-Recovered (SEIR) model and integrating machine learning based parameter optimization under epidemiological rational constraints. We used the model to predict the long-term reported cumulative numbers of COVID-19 cases in China from January 27, 2020. We evaluated our model on officially reported confirmed cases from three different regions in China, and the results proved the effectiveness of our model in terms of simulating and predicting the trend of the COVID-19 outbreak. In China-Excluding-Hubei area within 7 days after the first public report, our model successfully and accurately predicted the long trend up to 40 days and the exact date of the outbreak peak. The predicted cumulative number (12,506) by March 10, 2020, was only 3·8% different from the actual number (13,005). The parameters obtained by our model proved the effectiveness of prevention and intervention strategies on epidemic control in China. The prediction results for five other countries suggested the external validity of our model. The integrated approach of epidemic and machine learning models could accurately forecast the long-term trend of the COVID-19 outbreak. The model parameters also provided insights into the analysis of COVID-19 transmission and the effectiveness of interventions in China.

Condition for Global Stability for a SEIR Model Incorporating Exogenous Reinfection and Primary Infection Mechanisms.

A mathematical model incorporating exogenous reinfection and primary progression infection processes is proposed. Global stability is examined using the geometric approach which involves the generalization of Poincare-Bendixson criterion for systems of n-ordinary differential equations. Analytical results show that for a Susceptible-Exposed-Infective-Recovered (SEIR) model incorporating exogenous reinfection and primary progression infection mechanisms, an additional condition is required to fulfill the Bendixson criterion for global stability. That is, the model is globally asymptotically stable whenever a parameter accounting for exogenous reinfection is less than the ratio of background mortality to effective contact rate. Numerical simulations are also presented to support theoretical findings.

Bitcoin: SEIR-C Propagation Models of Block and Transaction Dissemination

Bitcoin can be modelled using the mathematics of biological systems. SEIR and SEIR-C models capture the propagation of transactions and blocks within the bitcoin network. With systems reacting as a susceptible or immune carrier, we can model the forces driving cycles of recurrent states. We demonstrate that we can analyse numerically the bitcoin network using a susceptible/exposed/infective/recovered (SEIR) epidemic model with seasonal transmission. Here, the system expresses a periodicity related to the discovery and propagation of blocks that can be extended into a competing epidemic model where blocks are discovered at a similar time or when transactions are double spent. In this paper, we introduce the concept of an SEIR model into the Bitcoin system and demonstrate how this can help in understanding the system.

Dynamics and Optimal Control of Ebola Transmission

A major Ebola outbreak occurs in West Africa since March 2014, being the deadliest epidemic in history. As an infectious disease epidemiology, Ebola is the most lethal and is moving faster than in previous outbreaks. On 8 August 2014, the World Health Organization (WHO) declared the outbreak a public health emergency of international concern. Last update on 7 July 2015 by WHO reports 27,609 cases of Ebola with a total of 11,261 deaths. In this work, we present a mathematical description of the spread of Ebola virus based on the SEIR (Susceptible–Exposed–Infective–Recovered) model and optimal strategies for Ebola control. In order to control the propagation of the virus and to predict the impact of vaccine programmes, we investigate several strategies of optimal control of the spread of Ebola: control infection by vaccination of susceptible; minimize exposed and infected; reduce Ebola infection by vaccination and education.

Modelling of transgenic mosquitoes and impact on malaria transmission

Transgenic mosquitoes that are resistant to malaria infection become one of the effective weapons to control malaria transmission. To investigate the impact of releasing transgenic mosquitoes on the malaria transmission, we first formulate mathematical models for interactive wild and transgenic mosquitoes based on systems of differential equations. We consider both dominant and recessive transgenes and include density-dependent vital rates in the mosquitoes population and provide fundamental analysis for the dynamics of the interactive mosquitoes. Using a simple compartmental SEIR (susceptible-exposed-infective-recovered) malaria transmission model as our baseline model, we then introduce transgenic mosquitoes into the baseline model. We study the dynamics of the simple baseline model and the models with the transgenic mosquitoes. Based on the reproductive numbers and endemic equilibria for these models, we investigate the impact of releasing transgenic mosquitoes on malaria transmission.

Analysis and control stratagems of flash disk virus dynamic propagation model

AbstractComputer virus mainly contain two kinds: network viruses and flash disk (FD) viruses, we name viruses as FD‐virus which spread by the latter way. Many researchers have studied the network virus in light with epidemiology such as susceptible‐infected‐susceptible, susceptible‐infected‐recovered, susceptible‐exposed‐infective‐recovered (SEIR) and susceptible‐infectious‐detected‐removed, but there are few studies on FD virus propagation. In this paper, a new dynamic propagation model of FD‐virus, namely FD‐SEIR, is discussed. Unlike other existing computer virus propagation models, FD‐SEIR mainly considers the FD‐virus propagation between host and FD, which is embodied by introducing the FD state and new propagation rate. Furthermore, several related dynamics properties are investigated, along with the analysis of how to control the FD‐virus prevalence based on the equilibrium stability. The simulation results show that the proposed model can serve as a basis for understanding and simulating FD‐virus epidemics. Copyright © 2011 John Wiley & Sons, Ltd.

Recurrent epidemics in small world networks

The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic susceptible-infective-recovered (SIR) model on complex networks. It was found that in addition to the reduction of the effective transmission rate, through the screening of infectives, spatial correlations have another major effect through the enhancement of stochastic fluctuations, which may become considerably larger than in the homogeneously mixed stochastic model. As a consequence, in finite spatially structured populations significant differences from the solutions of deterministic models are to be expected, since sizes even larger than those found for homogeneously mixed stochastic models are required for the effects of fluctuations to be negligible. Furthermore, time series of the (unforced) model provide patterns of recurrent epidemics with slightly irregular periods and realistic amplitudes, suggesting that stochastic models together with complex networks of contacts may be sufficient to describe the long-term dynamics of some diseases. The spatial effects were analysed quantitatively by modelling measles and pertussis, using a susceptible-exposed-infective-recovered (SEIR) model. Both the period and the spatial coherence of the epidemic peaks of pertussis are well described by the unforced model for realistic values of the parameters.

Malaria infection and human behavioral factors: A stochastic model analysis for direct observation data in the Solomon Islands.

The effect of human behavior on malaria infection was investigated in a holoendemic area in the Solomon Islands, using a newly developed mathematical model based on the results of blood examinations and 2 weeks of direct observations. The present study indicated that the place where individuals spent the evening had no significant relation to malaria infection, but that some kinds of clothes significantly reduced malaria infection. However, as the result of prediction by the Susceptible-Exposed-Infective-Recovered (SEIR) model, effective control of malaria transmission would require as much as 95% coverage by protection even in the case that the protective measure was highly effective. The results strongly suggested protection measures besides bed net distribution in addition to the necessity of health education. Am. J. Hum. Biol. 10:781-789, 1998. © 1998 Wiley-Liss, Inc.

Multiple attractors in the response to a vaccination program

Though it is well known that multiple attractors may co-exist in the SEIR (susceptible/exposed/infective/recovered) epidemic model with vital dynamics and seasonally forced oscillations in transmission, the epidemiological significance of multiple attractors has been a subject of debate. I show that the co-existence of attractors is relevant in using the model to study the dynamics of the introduction of a vaccination program into a stable epidemic cycle. Responses to the program may include more than one attractor. The exact timing of the introduction of the program relative to the original epidemic cycle is critical in determining which attractor appears in the response. Analysis of this simple model suggests that the role of multiple attractors in the response to vaccination should be examined in more realistic epidemiological models.

Seasonality and period-doubling bifurcations in an epidemic model

The annual incidence rates of some endemic infectious diseases are steady while others fluctuate dramatically, often in a regular cycle. In order to investigate the role of seasonality in driving cycles of recurrent epidemics, we analyze numerically the susceptible/exposed/infective/recovered (SEIR) epidemic model with seasonal transmission. We show that small amplitude periodic solutions exhibit a sequence of period-doubling bifurcations as the amplitude of seasonal variation increases, predicting a transition to chaos of the kind studied in other biological contexts. The epidemiological implication is that the seasonal mechanism generating biennial epidemics may not be able to account for small-amplitude recurrent epidemics of arbitrary periodicity.