SEI Model Research Articles

Air quality index induced nonsmooth system for respiratory infection

It has been observed that air pollution greatly affects respiratory infection and generates public health problem, but there are many challenges to quantifying the dynamics of air pollution and evaluating its impact on respiratory infections. A periodic Filippov system describing the state-dependent control strategy for air pollution, described by air quality index (AQI), is proposed. We theoretically analyze the non-autonomous Filippov subsystem for variation of AQI by converting into an autonomous Filippov system via increasing dimension of the system. We obtain that there is a unique periodic solution which is globally asymptotically stable. In particular, it shows that AQI stabilizes at either one of the periodic solutions of the free and control systems or a new periodic solution induced by the on-off control strategies, depending on the threshold levels. Then, a periodic system for respiratory infection with AQI-embedded transmission probability is formulated to examine the influence of air pollution on respiratory infection. We further obtain the control reproduction number (basic reproduction number with control strategies) of this periodic respiratory infection model. It is shown that the respiratory infection will go extinct if the control reproduction number is less than unity, while uniformly persists for larger than unity. The case study showed that the estimated threshold level coincides with the actual threshold which launches the traffic limitation measure in Xi’an, indicating the untimely density-dependent traffic limitation measure was ineffective in improving air quality. Numerically studies indicate that increasing the threshold level leads to an increase in the maximum value of the unique periodic solution for AQI and the control reproduction number for the AQI embedded SEIS model. These findings emphasize the importance of suitable threshold level to trigger interventions and suggest that untimely implementing control strategy may not effectively control air population.

Stochastic Modelling of Air Pollution Impacts on Respiratory Infection Risk.

The impact of air pollution on people's health and daily activities in China has recently aroused much attention. By using stochastic differential equations, variation in a 6year long time series of air quality index (AQI) data, gathered from air quality monitoring sites in Xi'an from 15 November 2010 to 14 November 2016 was studied. Every year the extent of air pollution shifts from being serious to not so serious due to alterations in heat production systems. The distribution of such changes can be predicted by a Bayesian approach and the Gibbs sampler algorithm. The intervals between changes in a sequence indicate when the air pollution becomes increasingly serious. Also, the inflow rate of pollutants during the main pollution periods each year has an increasing trend. This study used a stochastic SEIS model associated with the AQI to explore the impact of air pollution on respiratory infections. Good fits to both the AQI data and the numbers of influenza-like illness cases were obtained by stochastic numerical simulation of the model. Based on the model's dynamics, the AQI time series and the daily number of respiratory infection cases under various government intervention measures and human protection strategies were forecasted. The AQI data in the last 15months verified that government interventions on vehicles are effective in controlling air pollution, thus providing numerical support for policy formulation to address the haze crisis.

Stationary states and spatial patterning in the cellular automaton SEIS epidemiology model

We report computer simulation studies of the SEIS cellular automaton epidemiology model which takes into account explicitly the incubation period of the infection by considering separate fractions for the exposed E and infectious I individuals. The model is considered on a square lattice and the analysis is performed in various regimes covering cases of short and long incubation period at a range of contact rates. We found the critical curing rate to be independent on the incubation period, reflecting similarity between the SEIS model and the SI′S one, where I′=E+S. The stationary state of the lattice-based SEIS model compared to that of its compartment analogue indicates essential deviation between both at low contact rates. At long incubation period and high contact rates, the ratio between the values of E and I in a stationary state is found to depend strongly on the curing rate emphasizing the huge role of curing efficiency in this case. It was found that, upon approaching the critical curing rate, the time needed to reach a stationary state diverges, the effect reminiscent of critical slowing down. Visualization of the initial stage of the infection spread reveals porous clusters of infectious individuals with their surface decorated by exposed individuals.

An extended single particle model-based parameter identification scheme for lithium-ion cells

The accurate modeling and parameter identification of lithium-ion battery are of great significance in real-time control and high-performance operation for advanced battery management system (BMS) in electrified vehicles (EVs). However, it is difficult to obtain the information about the interior state inside battery, because it cannot be directly measured by some electric devices. In order to accurately identify the key state parameters of lithium-ion cell applied to electric ground vehicles, an extended single particle model of lithium-ion cell with electrolyte dynamics behaviors is first built up based on the porous electrode theory and concentration theory in this article. Compared with the conventional single particle cell model, the parameter description of the solid electrolyte interface film is incorporated into this model, and the coupled effects of temperature-dependent and electrolyte-dependent electrochemical parameters on the cell discharge are also taken into consideration. Based on this extended single particle cell model, a simplified parameter sensitivity analysis method and a comprehensive parameter identification scheme for lithium-ion cell are proposed herein, in which a sensitivity analysis of the capacity to a subset of electrochemical parameters that are hypothesized to evolve throughout the battery's life, is conducted to determine the highly sensitive parameters to be identified under some particular operation scenarios, and further to solve the parameter optimization problem using the genetic algorithm. Based on this method, the test data under the working condition of 1 C discharge rate at 23℃ are employed to evaluate the identified parameters of lithium-ion battery cell with a peak value of voltage error less than 3.8%. Afterwards, the effectiveness and feasibility of the proposed parameter identification scheme are validated by the comparative study of the simulated output voltage and the experimental output voltage under the same input current profile. Specifically, the 0.05 C discharge and HPPC (hybrid pulse power characterization) current profile are used to verify the evaluated parameters under the 1 C discharge condition, and the maximum relative errors of voltage with 0.05 C galvanostatic discharge profile at 23 and 45℃ are 3.4% and 2.6% by using our proposed SPMe_SEI model, and 5.7% and 4.0% by using the traditional SPMe model, respectively. Moreover, the maximum relative errors of voltage with HPPC discharge profile at 23 and 45℃ are 1.9% and 1.5% by using our proposed SPMe_SEI model, and 2.1% and 1.8% by using the traditional SPMe model, respectively. It is concluded that the proposed parameter identification scheme for a lithium-ion cell model can provide a solid theory foundation for facilitating the estimation of state-of-health in BMS application.

Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission Rate of Disease

We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic (R0) and stochastic (R0) basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., R0<1), epidemic can still grow initially (if R0>1) because of the presence of noise in the stochastic version of the model. That is, diffusion rates can have effect on the stability by causing a transient epidemic advance. A threshold criterion for epidemic invasion was derived in the presence of external noise.

SEIS model with multiple latent stages and treatment in an exponentially growing population

An SE^{n}IS epidemiological model with vital dynamics in an exponentially growing population is discussed. Without treatment three threshold parameters $R_0, R_1$ and $R_2$ determine the dynamic of compartments sizes and that of the fractions. With the treatment the dynamics of the population and that of the epidemic depend on three other threshold parameters $R_T, R_{1T}$ and $R_{2T}$. We made a link between the models with one latent stage and the models with multiple latent stages by defining and deriving the effective activation rate and the effective treatment rate for the latent individuals. We defined the treatment force, the relative treatment force and deduced the critical treatment force needed to eradicate the disease. The theoretical results are validated by numerical simulations. https://doi.org/10.28919/cmbn/3436

A model for hepatitis B disease with age-dependent susceptibility and vertical transmission

In this paper, we construct a SEI model for hepatitis B where the susceptibility and transmission probabilities depend on the chronological age. We extend results of (Houpa et al, 2014) who studied it without vertical transmission. Moreover, we derive the basic reproductive rate R0. Under given assumptions, we prove that the disease free equilibrium is globally asymptotically stable if R0 <1; the endemic equilibrium is globally asymptotically stable if R0 >1 and that the system is uniformly persistent. Numerical simulations are carried out to illustrate our results.https://doi.org/10.28919/cmbn/3126

The impact of hesitation on passive worm spreading in P2P networks

P2P file-sharing networks allow peers (computers) to download files and make them available to other users on the network. The fear of downloading worm file is a reasonable reason to discourage users to utilize P2P file-sharing networks. So, peers may hesitate to open the downloaded files due to the concern of receiving poisoned files or being compromised by malwares. In this article, we present a model of spread of passive worm in P2P file-sharing networks, where susceptible peers which were already infected before, are reluctant to open new downloaded files. Here, we address this issue by introducing a modified SEIS model, where λe (average rate at which exposed peer opens a downloaded file) decreases with the number of reinfections n for a maximum of l times (λe(n+1) = 𝜖λe(n)where 0<𝜖<1represents the hesitation value). Hence, for a susceptible peer which was already infected by the worm, the hesitation to open a new downloaded file is quantified by the two parameters (𝜖,l). We studied numerically the effects of various system parameters on the time evolution of the peer states. At steady state and for every value of l, there exists a critical value 𝜖c below which the system is infection-free. A phase diagram in the plane (𝜖,l) is constructed that shows which phases are present according to the state variables. In addition, we introduced and evaluated the effect of different patch-based immunization strategies to show how they could block the spread of the worm in the system. The immunization patch is launched in the network at a time tl and will be out of order at a time tf (i.e. outdated patch). We found that the parameters (tl,tf, 𝜖) are very important to be defined when developing the immunization patch.

Characterizing and Discovering Spatiotemporal Social Contact Patterns for Healthcare.

During an epidemic, the spatial, temporal and demographic patterns of disease transmission are determined by multiple factors. In addition to the physiological properties of the pathogens and hosts, the social contact of the host population, which characterizes the reciprocal exposures of individuals to infection according to their demographic structure and various social activities, are also pivotal to understanding and predicting the prevalence of infectious diseases. How social contact is measured will affect the extent to which we can forecast the dynamics of infections in the real world. Most current work focuses on modeling the spatial patterns of static social contact. In this work, we use a novel perspective to address the problem of how to characterize and measure dynamic social contact during an epidemic. We propose an epidemic-model-based tensor deconvolution framework in which the spatiotemporal patterns of social contact are represented by the factors of the tensors. These factors can be discovered using a tensor deconvolution procedure with the integration of epidemic models based on rich types of data, mainly heterogeneous outbreak surveillance data, socio-demographic census data and physiological data from medical reports. Using reproduction models that include SIR/SIS/SEIR/SEIS models as case studies, the efficacy and applications of the proposed framework are theoretically analyzed, empirically validated and demonstrated through a set of rigorous experiments using both synthetic and real-world data.

Global stability of an SEI model for plant diseases

Abstract We propose an SEI epidemic model for plant diseases, which incorporates disease latency, disease-caused removal, and constant recruitment in both susceptible and exposed classes. Because of the recruitment and disease-caused removal, the total population is varying. It is shown that the model only has an endemic equilibrium and the equilibrium is globally stable.

Global stability for an SEI model of infectious disease with immigration

We study an SEI model of disease transmission with immigration into all three classes. For incidence, we allow for a nonlinear response to the number of infectives, including mass action and saturating incidence as special cases. There is no disease-free equilibrium and therefore no basic reproduction number. For all parameter values, the only equilibrium is an endemic equilibrium. Using a Lyapunov function, we show that this equilibrium is globally asymptotically stable.

Multilayer Separator for Lithium Batteries

Lithium metal provides the highest specific energy density and would be a perfect anode material for a lithium ion battery [1]. But so far only polymer batteries based on PEO show a stable interaction with lithium metal [2-3]. However, these electrolytes feature only a low ionic conductivity (up to 10-3 S cm-1) at room temperature. To use lithium metal in combination with liquid electrolytes, a thin layer (10 μm) of polyethylene oxide (PEO) was coated on conventional separators. A simple, solvent free technique was used to combine the polymer electrolyte to the separator (patent pending). To enhance the mechanical stability during the swelling with electrolyte, the polymer was cross-linked after the coating step [4].An application of the polymer/separator system is possible with established positive electrode materials like lithium iron phosphate (LFP) or lithium nickel manganese cobalt oxide (NMC) to enhance the energy density of the system. Even more promising is the use in next generation battery systems like lithium air and lithium-sulfur. The thin layer of PEO optimizes the lithium-electrolyte interface and therefore acts as a protective layer against parasitic reactions like electrolyte decomposition [5]. In Li-O2and Li-S batteries, the PEO could additionally act as a barrier against, respectively, oxygen or polysulfide diffusion to the lithium anode.The PEO layer was found to be mechanically stable during cell assembling and electrolyte application. Due to the cross-linking, even an excess of electrolyte does not dissolve the polymer. By chemical bonding between the PEO and polyethylene (PE) or polypropylene (PP) a loss of connection between the two separator layers is prevented. Partly impregnation of PEO into porous ceramic separators during the coating process shows the same effect after cross-linking. Differential scanning calorimetry (DSC) tests show that PEO and ionic liquids form an amorphous layer on the lithium surface, similar to ternary polymer electrolytes [6].To verify the electrochemical stability of the PEO on the lithium metal surface, stripping-plating tests in symmetrical lithium cells were performed with a broad range of electrolytes. For established cathode materials, carbonate-based solvents like ethylene carbonate (EC) and dimethyl carbonate (DMC) with lithium hexafluorophosphate (LiPF6) were investigated. For next generation batteries or cycling at higher temperatures, tests with tetraethylene glycol dimethyl ether (TEGDME), 1,3-dioxolane and ionic liquids like 1-butyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (Pyr14TFSI) with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) were performed. Finally, cycling tests with NMC and sulfur cathodes were performed.1. Bruce, P.G., et al., Li-O2 and Li-S batteries with high energy storage. Nat Mater, 2012. 11(02): p. 172-172.2. Li, Z., et al., A review of lithium deposition in lithium-ion and lithium metal secondary batteries.Journal of Power Sources, (0).3. Kim, G.T., et al., UV cross-linked, lithium-conducting ternary polymer electrolytes containing ionic liquids. Journal of Power Sources, 2010. 195(18): p. 6130-6137.4. Rupp, B., et al., Polymer electrolyte for lithium batteries based on photochemically crosslinked poly(ethylene oxide) and ionic liquid. European Polymer Journal, 2008. 44(9): p. 2986-2990.5. Peled, E., et al., The sei model—application to lithium-polymer electrolyte batteries. Electrochimica Acta, 1995. 40(13–14): p. 2197-2204.6. Joost, M., et al., Phase stability of Li-ion conductive, ternary solid polymer electrolytes. Electrochimica Acta, 2013. 113(0): p. 181-185.

A model for hepatitis B disease with age-dependent susceptibility

In this paper, a SEI model for hepatitis B is constructed in a closed population where the susceptibility depends on the chronological age and the basic reproduction rate R0is derived. Under suitable (biological and mathematical) assumptions, it is shown that the disease free equilibrium is globally asymptotically stable (GAS) if R0 1 induces that endemic equilibrium is GAS and the system is uniformly persistent.

A General Model for Hepatitis B Disease with Age-Dependent Susceptibility and Transmission Probabilities

A SEI model for hepatitis B is constructed where the susceptibility and other crucial transmission probabilities depend on the chronological age and the basic reproduction rate R0 is derived. Under suitable (biological and mathematical) assumptions in a closed population, results of Houpa D. D. E. et al. [1] are extended from constant case of p and q to age-dependent case: the disease-free equilibrium is globally asymptotically stable (GAS) if R0 . On the other hand, R0 > 1 induces that endemic equilibrium is GAS and the system is uniformly persistent.

On a Stochastic SEIS Model with Treatment Rate of Latent Population

The asymptotic dynamics of a stochastic SEIS epidemic model with treatment rate of latent population is investigated. First, we show that the system provides a unique positive global solution starting from the positive initial value. Then, the long-term asymptotic behavior of the model is studied: ifR0, which is called the basic reproduction number of the corresponding deterministic model, is not more than unity, the solution of the model is oscillating around the disease-free equilibrium of the corresponding deterministic system, whereas ifR0is larger than unity, we show how the solution spirals around the endemic equilibrium of deterministic system under certain parametric restrictions. Finally, numerical simulations are carried out to support our theoretical findings.

Global stability of a multi-group SEI model

In this paper, a multi-group SEI model with the bilinear incidence and variable susceptibility and infectivity is analyzed. The susceptible individuals are divided into n groups according to their susceptibility, and infected individuals are divided into m groups according to infectivities. Each group of infected individuals has an exposed period. The basic reproduction number R0 is obtained, and globally asymptotic stability of disease-free equilibrium is proved if R0⩽1. If R0>1, the disease-free equilibrium is unstable and the endemic equilibrium exists and is unique, which is globally asymptotically stable. Finally, some numerical examples are given to illustrate the above analysis.

A discrete-time analogue preserving the global stability of a continuous SEIS epidemic model

In this paper, we show dynamical consistency between the continuous SEIS epidemic model and its discrete-time analogue, that is, both global dynamics of a continuous SEIS epidemic model ‘without delays’ and the positive solutions of the corresponding backward Euler discretization with mesh width are fully determined by the same single-threshold parameter which is the basic reproduction number of the continuous SEIS model. To prove this, we first obtain lower positive bounds for the permanence of this discrete-time analogue for and then apply a discrete version of Lyapunov function technique in the paper [12].

The dynamics of a delayed pest management SEI system with impulsive harvesting at different moments

According to biological strategy for pest control, we consider a delayed pest management SEI model with birth pulse and impulsive harvesting at different moments. We prove that all solutions of the system are uniformly ultimately bounded and get the conditions of the globally attractive infection-free boundary periodic solution of the system. Further, we obtain sufficient condition with time delay for the permanence of the system. Our results give some reasonable suggestions for pest

The basic reproduction number of discrete SIR and SEIS models with periodic parameters

Seasonal fluctuations have been observed in many infectious diseases.Discrete epidemic models with periodic epidemiological parameters are formulated and studiedto take into account seasonal variations of infectious diseases.The definition and the formula of the basic reproduction number $R_0$ are given by following the framework in [1,2,3,4,5].Threshold results for a general model are obtained which show that the magnitude of $R_0$ determineswhether the disease will go extinct (when $R_01$) in the population.Applications of these general results to discrete periodic SIR and SEIS models are demonstrated.The disease persistence and the existence of the positive periodic solution are established.Numerical explorations of the model properties are also presented via several examplesincluding the calculations of the basic reproduction number, conditions for the disease extinction or persistence,and the existence of periodic solutions as well as its stability.

Dynamic Modeling and Analysis of the Email Virus Propagation

A novel deterministic SEIS model for the transmission of email viruses in growing communication networks is formulated. Interestingly, the model is different from classical SEIS models not only in the form, but also in the dynamical features. We study the equilibria and their stability and analyse the bifurcation dynamics of the model. In particular, we find that the virus‐free equilibrium is locally asymptotically stable for any parameter values, which may attribute to the absence of the basic reproduction number. It is shown that the model undergoes a saddle‐node bifurcation and admits the bistable phenomenon. Moreover, on the basis of the Lyapunov function, the domains of attraction of equilibria are estimated by solving an LMI optimization problem. Based on the above theoretical results, some effective strategies are also provided to control the propagation of the email viruses. Additionally, our results are confirmed by numerical simulations.