On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties

Abstract

A new discrete SEIADR epidemic model is built based on previous continuous models. The model considers two extra subpopulation, namely, asymptomatic and lying corpses on the usual SEIR models. It can be of potential interest for diseases where infected corpses are infectious like, for instance, Ebola. The model includes two types of vaccinations, a constant one and another proportional to the susceptible subpopulation, as well as a treatment control applied to the infected subpopulation. We study the positivity of the controlled model and the stability of the equilibrium points. Simulations are made in order to provide allocation and examples to the different possible conditions. The equilibrium point with no infection and its stability is related, via the reproduction number values, to the reachability of the endemic equilibrium point.

On a SIR Model in a Patchy Environment Under Constant and Feedback Decentralized Controls with Asymmetric Parameterizations

“…Proposition (ii) has been proved. To prove Property (iii), assume that there is an attainable (i.e., with no negative component) endemic equilibrium point if R 0 < 1 and note, from Equations (1), (14) and (15), that…”

“…This is the case, for instance, if an additional treatment control is injected on the infectious subpopulation. See, for instance [14,15].…”

“…In [13], some useful numerical tools are given concerning the non-singularity of perturbed matrices which are used in this paper. Background literature on dynamic systems, including its role on epidemic modelling, is given in [14][15][16][17][18][19]. In this context, typical situations which need relevant attention when dealing with epidemic models, thinking of their usefulness in their practical implementation in health centers are:…”

“…(a) The implementation of mixed constant and feedback controls with eventual alternative controller parameterizations and supervisory switching actions between them according to optimization trade-off criteria on the vaccine costs, or their availability, and the infection evolution through time [15,20]. The supervisory scheme chooses online the best appropriate controller parameterization that minimizes the loss function.…”

Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

“…Mathematically, there are various reports on the modeling of the propagation of diseases [13][14][15][16]. In addition to reports on the modeling of the transmission of hepatitis B [10,17], there are also studies on the co-dynamics of pneumonia and typhoid fever diseases with cost effective optimal control analysis [18], the mathematical modeling of hepatitis C treatment for injecting drug users [19] and the epidemiological modeling of the propagation of cholera with optimal control treatment [20].…”