Global stability analysis for a model with carriers and non-linear incidence rate

Gómez, Miller Cerón; Mondragón, Eduardo Ibarguen; Molano, Patricia Lopez

doi:10.1080/17513758.2020.1772998

Cited by 10 publications

(4 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kuddus and Rahman applied a similar approach to analyze COVID-19 using an SLIR model with saturated nonlinear incidence, as detailed in [22]. Gomez et al,in [11], examined the global stability of a model that categorized populations into susceptible, carriers (asymptomatic), infectious, and recovered (SCIR).…”

Section: Introductionmentioning

confidence: 99%

Global analysis for a modified SEIR model with general non-linear incidence function

Mohamed,

Ahmedou,

Elemine Vall

2024

Nonlinear Dyn

View full text Add to dashboard Cite

This study introduces a segmented mathematical model, crafted for dissecting the spread mechanisms of a specific disease. It refines the classic SEIR framework by bifurcating the infected segment (I) into two subcategories: the uneducated infected (Iu) and the educated infected (Ie). Central to this model is a complex infection rate function, delineated as f (S) (g(Iu) + h(Ie)). Critical to our analysis are certain presumptions regarding the functions f , g, and h. By utilizing the next generation matrix technique, we successfully derived the fundamental reproduction rate, denoted as R0. The research confirms the existence of two vital states of equilibrium within the model: one signifying the absence of disease and the other, its persistent presence. The global asymptotic stability of these equilibriums is validated using Lyapunov's direct method coupled with LaSalle's invariance principle. To reinforce our theoretical findings, we executed a series of numerical simulations, applying specific variations of the functions f , g, and h.

show abstract

Section: Introductionmentioning

confidence: 99%

Global analysis for a modified SEIR model with general non-linear incidence function

Mohamed,

Ahmedou,

Elemine Vall

2024

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…[9,12,21,25,28,34,41,45,46], H.C. [14,23,24] and I.C. [22,25,26,44] and the other control [1,3,10,18,40,42]. Nevertheless, in this manuscript, we design a SIR epidemic system to address the D.T.C.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

Alsaedi³

et al. 2023

Preprint

View full text Add to dashboard Cite

This paper investigates the global dynamic behavior and bifurcations of a classical nonlinear transmission SIR epidemic model with discontinuous threshold strategy. Different from previous results, we not only consider the general nonlinear transmission, but also adopt the discontinuity control. First, the positivity and boundedness of the model are given. Second, by employing Lyapunov LaSalle approach and using Green Theorem, we perform the globally stable the three types of equilibria of the system. We analytically show the orbit can tend to the disease-free equilibrium point, the endemic equilibrium point or the sliding equilibrium point in discontinuous surfaces of the system. In addition, we also analyze the sliding bifurcations of the model when consider the special transmission. Finally, some numerical simulations are worked out to confirm the results obtained in this paper.

show abstract

“…A SEIR type age-structured model with migration and nonlinear incidence rates was studied in [32]. While models where asymptomatic people transmit the disease and consider non-linear incidence rates but do not consider immigration have been studied in [7,8,21].…”

Section: Introductionmentioning

confidence: 99%

Mathematical model of a SCIR epidemic system with migration and nonlinear incidence function

Gómez¹,

Mondragón²,

Rubio³

2023

J. Math. Computer Sci.

View full text Add to dashboard Cite

In this paper, we proposed a generalization for a model that considers Susceptible, Infected, Carrier, and Recovered by introducing a general incidence rate and considering migration in all its populations. This model has the characteristic that carriers and infected can transmit the disease, besides it has not a disease-free equilibrium point and no basic reproductive number. The focus of this study is to show a generalized model and the conditions required to analyze the equilibrium point stability. Using an appropriate Lyapunov function and with suitable conditions on the functions involved in the general incidence, we showed that the disease equilibrium point is globally asymptotically stable. Also, we presented numerical simulations of two applications to illustrate the results obtained from the analytical part.

show abstract

Global stability analysis for a model with carriers and non-linear incidence rate

Cited by 10 publications

References 24 publications

Global analysis for a modified SEIR model with general non-linear incidence function

Global analysis for a modified SEIR model with general non-linear incidence function

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

Mathematical model of a SCIR epidemic system with migration and nonlinear incidence function

Contact Info

Product

Resources

About