A continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account

The global analysis of a spatio-temporal fractional order SEIR infection epidemic model is studied and analyzed in this paper. The dynamics of the infection is described by four partial differential equations with a fractional derivative order and with diffusion. The equations of our model describe the evolution of the susceptible, the exposed, the infected and the recovered individuals with taking into account the spatial diffusion for each compartment. At first, we will prove the existence and uniqueness of the solution using the results of the fixed point theorem, and the equilibrium points are established and presented according to R0. Next, the bornitude and the positivity of the solutions of the proposed model are established. Using the Lyapunov direct method it has been proved that the global stability of the each equilibrium depends mainly on the basic reproduction number R0. Finally, numerical simulations are performed to validate the theoretical results.

Section: The Equilbriamentioning

confidence: 99%

“…Most of the classical models take into account only the temporal variable t [9][10][11][12]. However, the time t is not the only variable that influences the infection propagation.…”

Section: Introductionmentioning

confidence: 99%

Global dynamic of spatio-temporal fractional order SEIR model

Bounkaicha¹,

Allali²,

Tabit³

et al. 2023

“…By using a discrete version of Pontryagin's maximum principle [30][31][32], we derive the necessary conditions for our optimal controls. For this purpose, we define the Hamiltonian as…”

Section: Necessary Conditionsmentioning

confidence: 99%

“…, 6, the adjoint variables satisfying the following equations Proof. Using the discrete version of Pontryagin's maximum principle [33][34][35][36][37] we obtain the following adjoint equations:…”

Section: Necessary Conditionsmentioning

confidence: 99%

A discrete mathematical model SIRS with the evolution of regions to attack infectious diseases

Benfatah,

Khaloufi,

Boutayeb

et al. 2023

This paper presents a new SIRS mathematical model describing the evolution of an infectious disease, assuming that the spatial supports of this infection are also evolutionary and obey a compartmental model. We propose four control strategies to manage the spread of the disease among individuals and regions. The Pontryagin maximum principle is employed to characterize the optimal controls, and the optimality system is solved using an iterative approach. Finally, numerical simulations are conducted to validate the theoretical analysis using MATLAB.

“…Mathematical modelling is one of the most necessary functions that contribute to the representation and simulation of ecological, social, economic phenomena and Epidemics [11][12][13][14], and convert them into mathematical equations formulated, studied, analysed, and interpreted their results. Kada Driss et al [15], discussed the spread of addiction to electronic games phenomenon and proposed a discrete mathematical model with control strategies to limit the spread of gaming addiction.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

Kada¹,

Kouidere²,

Balatif³

et al. 2023

Self Cite

In this article, we propose a PEARM mathematical model to depict the dynamic of a population that reacts in the spread of the gaming disorder with media coverage. The basic reproduction number and existence of free equilibrium point and endimec equilibrium point are obtained with same fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated. By using Routh–Hurwitz criteria, the local stability of free equilibrium point and endimec equilibrium point are obtained. Also, we propose an optimal strategy to implement the optimal campaigns through directing children and adolescents to educational and entertaining alternative means, and creating centers to restore the rehabilitation of addicts to electronic games. The existence of the optimal control are obtained by Pontryagain's maximum principle. Finally, some numerical simulations are also performed to illustrate the theoretical analysis of our results, using Matlab software. Our results show that media coverage is an effective measure to quit electronic gaming disorder.