Observer‐Based Vaccination Strategy for a True Mass Action SEIR Epidemic Model with Potential Estimation of All the Populations

Abstract

This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among the susceptible and infected. The control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e., susceptible plus infected plus infectious) to asymptotically converge to zero. A state observer is used to estimate the true various partial populations of the susceptible, infected, infectious, and immune which are assumed to be unknown. The model parameters are also assumed to be, in general, unknown. In this case, the parameters are replaced by available estimates to implement the vaccination action.

Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination

“…As we all known, some diseases may be governed directly or indirectly by environmental factors such as temperature, humidity, and barometric pressure; see [9][10][11][12][13], for example. It is realistic to investigate this kind of epidemic models with periodic (seasonal) fluctuations.…”

Sliding mode robust control of SEIR epidemic models

“…Thus, different types of vaccination laws based on Control Theory have appeared in the literature during the last years such as the state-feedback control [2], feedback linearization [1], [3] and observer-based control [4]. In addition, pulse vaccination has also gained much attention during the last decade, [5], mainly for its successful application in the eradication of poliomyelitis and measles across Central and South America, [5].…”

State estimators for some epidemiological systems

“…Earlier work using observers in an epidemiological context dates back at least to the works of Velasco-Hernandez and collaborators (Alvarez-Ramirez et al, 2000;Velasco-Hernández et al, 2002, for an HIV model); since 2012 there is a growing interest in the literature, and more recent work includes: Bichara et al (2014) (for a malaria's intra-host model), Tami et al (2013); Abdelhedi et al (2014Abdelhedi et al ( , 2016; De la Sen et al (2011) (for some SEIR models), (for a SI-SI Dengue epidemic model), Diaby et al (2015) (for a schistosomiasis infection model), Bliman and D'Avila Barros (2017); Aronna and Bliman (2018); (interval-observer for uncertain SIR and SIR-SI models) and De la Sen et al (2011);Alonso-Quesada et al (2012); Ibeas et al (2015) (for SEIR models with vaccination in discrete and continuous time with vaccination) .…”