A New COVID-19 Pandemic Model including the Compartment of Vaccinated Individuals: Global Stability of the Disease-Free Fixed Point

Al-Shbeil, Isra; Djenina, Noureddine; Jaradat, Ali; Al-Husban, Abdallah; Ouannas, Adel; Grassi, Giuseppe

doi:10.3390/math11030576

Cited by 13 publications

(10 citation statements)

References 27 publications

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“…The overarching multi-objective is to minimize the risks associated with disease transmission and economic volatility. Dasaratha (2023) in [20] analyzes the spread of a contagious disease when behavior responds to the disease's prevalence, while Al-Shbeil et al (2023) [21] prove the disappearance of the pandemic, provided that an inequality involving the vaccination rate is satisfied.…”

Section: Introductionmentioning

confidence: 99%

Optimal Social and Vaccination Control in the SVIR Epidemic Model

Ramponi,

Tessitore

2024

Mathematics

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In this paper, we introduce an approach to the management of infectious disease diffusion through the formulation of a controlled compartmental SVIR (susceptible–vaccinated–infected–recovered) model. We consider a cost functional encompassing three distinct yet interconnected dimensions: the social cost, the disease cost, and the vaccination cost. The proposed model addresses the pressing need for optimized strategies in disease containment, incorporating both social control measures and vaccination campaigns. Through the utilization of advanced control theory, we identify optimal control strategies that mitigate disease proliferation while considering the inherent trade-offs among social interventions and vaccination efforts. Finally, we present the results from a simulation-based study employing a numerical implementation of the optimally controlled system through the forward–backward sweep algorithm. The baseline model considered incorporates parameters representative of typical values observed during the recent pandemic outbreak.

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Section: Introductionmentioning

confidence: 99%

Optimal Social and Vaccination Control in the SVIR Epidemic Model

Ramponi,

Tessitore

2024

Mathematics

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“…Epidemic models can also be applied for the description of other processes, such as the spread of ideas (for overviews, see [ 3 , 63 ]). We also note the use of epidemic models for the study of COVID-19 spreading [ 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 ], as well as the numerical methods for obtaining solutions to such models [ 79 , 80 ].…”

Section: Introductionmentioning

confidence: 99%

Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics

Vitanov

2023

Entropy

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The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities. The equations from the obtained sequence are treated by the Simple Equations Method (SEsM). This allows us to obtain exact solutions to some of these equations. We discuss several of these solutions. Some (but not all) of the obtained exact solutions can be used for the description of the evolution of epidemic waves. We discuss this connection. In addition, we use two of the obtained solutions to study the evolution of two of the COVID-19 epidemic waves in Bulgaria by a comparison of the solutions with the available data for the infected individuals.

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“…Epidemic models can be applied to study other processes as well, such as the spread of ideas (for overviews, see [4,54]). An important recent application of epidemic models is in research on the spread of COVID-19 [55][56][57][58][59][60][61][62][63][64][65][66][67][68]. We proceed as follows: the methodology of SEsM is described briefly in Section 2; in Section 3, we derive a sequence of nonlinear differential equations connected to the SEIR model of epidemic spread and use SEsM to obtain exact solutions of these equations; and in Section 4, the applicability of the obtained solutions for describing the evolution of epidemic waves is discussed.…”

Section: Introductionmentioning

confidence: 99%

Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics

Vitanov

Dimitrova

2023

Computation

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We studied obtaining exact solutions to a set of equations related to the SEIR (Susceptible-Exposed-Infectious-Recovered) model of epidemic spread. These solutions may be used to model epidemic waves. We transformed the SEIR model into a differential equation that contained an exponential nonlinearity. This equation was then approximated by a set of differential equations which contained polynomial nonlinearities. We solved several equations from the set using the Simple Equations Method (SEsM). In doing so, we obtained many new exact solutions to the corresponding equations. Several of these solutions can describe the evolution of epidemic waves that affect a small percentage of individuals in the population. Such waves have frequently been observed in the COVID-19 pandemic in recent years. The discussion shows that SEsM is an effective methodology for computing exact solutions to nonlinear differential equations. The exact solutions obtained can help us to understand the evolution of various processes in the modeled systems. In the specific case of the SEIR model, some of the exact solutions can help us to better understand the evolution of the quantities connected to the epidemic waves.

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A New COVID-19 Pandemic Model including the Compartment of Vaccinated Individuals: Global Stability of the Disease-Free Fixed Point

Cited by 13 publications

References 27 publications

Optimal Social and Vaccination Control in the SVIR Epidemic Model

Optimal Social and Vaccination Control in the SVIR Epidemic Model

Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics

Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics

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