About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls

Abstract

This paper studies some basic properties of an SEIR (Susceptible-Exposed-Infectious-Recovered) epidemic model subject to vaccination and treatment controls. Firstly, the basic stability, boundedness, and nonnegativity of the state trajectory solution are investigated. Then, the problem of partial state reachability from a certain state value to a targeted one in finite time is focused on since it turns out that epidemic models are, because of their nature, neither (state) controllable from a given state to the origin nor reachable from a given initial condition. The particular formal statement of the partial reachability is focused on as a problem of output-reachability by defining a measurable output or lower dimension than that of the state. A special case of interest is that when the output is defined as the infectious subpopulation to be step-to-step tracked under suitable amounts being compatible with the required constraints. As a result, and provided that the output-controllability Gramian is nonsingular on a certain time interval of interest, a feedback control effort might be designed so that a prescribed value of the output can be approximately tracked. A linearization approximation is performed to simplify and facilitate the above task which is based on a point-to-point linearization of the solution trajectory. To this end, an “ad hoc” sampled approximate output trajectory is defined as control objective to be targeted through a point-wise calculated Jacobian matrix. A supervised appropriate restatement of the targeted suited sampled output values is redefined, if necessary, to make the initial proposed sampled trajectory compatible with the various needed constraints on nonnegativity and control boundedness. The design can be optionally performed under constant or adaptive sampling rates. Finally, some numerical examples are given to test the theoretical aspects and the design efficiency of the model.

SEIARN: Intelligent Early Warning Model of Epidemic Spread Based on LSTM Trajectory Prediction

“…Chen et al [9] proposed a time-dependent SIR model, which tracks the transmission and recovery rate of time t. Gu et al [10] proposed the establishment of a SEIR transmission dynamics model considering the virus transmission capacity of patients in the incubation period and tracking the impact of isolation interventions on the epidemic. Radulescu and Manuel et al [11,12], respectively, adapted the traditional SEIR epidemic model to the specific dynamic compartment and epidemic parameters of COVID-19 and studied some basic characteristics of the SEIR epidemic model affected by vaccination and treatment control. Wang et al [13] introduced the concept of asymptomatic infected persons and proposed to build a SEIADR model, which has better fitting effect and authenticity.…”

“…Since the outbreak of the epidemic, scholars at home and abroad have carried out relevant research on the transmission models of novel coronavirus. Most of these models are based on classical infectious disease models, such as the mathematical model of infectious disease dynamics SIR model [7][8][9], SEIR model [2][3][4][5][6][10][11][12], and SEIAR model. [13][14][15][16][17][18][19][20], which divide the population into susceptible s, latent e, infectious I, confirmed J, and rehabilitated R groups.…”

Dynamics of a Novel IVRD Pandemic Model of a Large Population over a Long Time with Efficient Numerical Methods

“…Moreover, see [3] for verification of the behavior of the model with susceptible and exposed populations. Some of the works that motivated this present research include a heat transfer model developed using a fractional derivative [4], the use of the Laplace Adomian Decomposition method (LADM) to analyze an SEIR model for the first time [5], a COVID-19 model using the fractional derivative [6], research into the existence and uniqueness of nonlinear epidemiology applications [7], an SEIR model using vaccination strategy and a fractional order [8], a COVID-19 model under the lockdown strategy [9], an SIR model following the social distancing strategy [10], an Indonesian SIR COVID-19 epidemic fuzzy model [11], a Stiff Fuzzy COVID-19 model under the 14-day transmission model [1], a new fractional epidemic model dealing with a death population [12], as well as an LADM for solving a model for HIV infection of CD4 + T cells [13], a fractional SEIQ with delay [14], a fractional model of dengue transmission [15], and a discrete COVID-19 stochastic model [16]. Recently, authors including Mathews, Vitaly, and many others [17][18][19][20][21][22][23][24][25] have started to work on epidemic modeling, especially on models for COVID-19.…”

Design a robust sliding mode controller based on the state and parameter estimation for the nonlinear epidemiological model of Covid-19

“…The effect of social distance is analyzed in the mitigation of disease spread. In [23][24][25][26][27], the authors consider the effect of vaccination in modeling the disease outbreak. These models help us to understand how global vaccination reduces the rate of mortality.…”