Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay

Kashkynbayev, Ardak; Rihan, Fathalla A.

doi:10.3390/math9151829

Cited by 9 publications

(3 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution u = U 3 (x, t) was obtained using Formula (43), where ψ ≡ 1, and ϕ is the corresponding solution of the linear ODE (44).…”

Section: Test Problem 2 It Can Be Shown By Direct Verification That E...mentioning

confidence: 99%

“…The simplest ordinary differential equation (ODE) with delay has the form u t = F(u, w), w = u(t − τ), (1) where F is a function. Delay ODEs arise in population theory , medicine [24][25][26][27][28][29][30][31][32][33][34][35], epidemiology [36][37][38][39][40][41][42][43][44], economy [45][46][47][48], climatology [49], mechanics [50], control theory [51], the mathematical theory of artificial neural networks [52][53][54][55][56][57], etc. However, the processes occurring in such systems are often spatially inhomogeneous, which leads to the use of more complex reaction-diffusion equations (RDEs) with a constant delay (see, e.g, [58,59]):…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

Сорокин

Vyazmin

2022

Mathematics

View full text Add to dashboard Cite

The paper describes essential reaction–diffusion models with delay arising in population theory, medicine, epidemiology, biology, chemistry, control theory, and the mathematical theory of artificial neural networks. A review of publications on the exact solutions and methods for their construction is carried out. Basic numerical methods for integrating nonlinear reaction–diffusion equations with delay are considered. The focus is on the method of lines. This method is based on the approximation of spatial derivatives by the corresponding finite differences, as a result of which the original delay PDE is replaced by an approximate system of delay ODEs. The resulting system is then solved by the implicit Runge–Kutta and BDF methods, built into Mathematica. Numerical solutions are compared with the exact solutions of the test problems.

show abstract

“…The solution u = U 3 (x, t) was obtained using Formula (43), where ψ ≡ 1, and ϕ is the corresponding solution of the linear ODE (44).…”

Section: Test Problem 2 It Can Be Shown By Direct Verification That E...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

Сорокин

Vyazmin

2022

Mathematics

View full text Add to dashboard Cite

show abstract

“…However, researchers looked at the dynamic behavior of a cancer model in a polluted environment while taking into account the time lag it took for the environment to be cleared of contamination [27]. Many other studies of epidemic models including delay role are available, for example, [28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Dynamics Analysis of a Delayed Crimean‐Congo Hemorrhagic Fever Virus Model in Humans

Al-Jubouri,

Naji

2024

Journal of Applied Mathematics

View full text Add to dashboard Cite

Given that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier “tick,” studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease’s incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution’s qualitative attributes is included. According to the established basic reproduction number, the stability analysis of the endemic equilibrium point and the disease-free equilibrium point is examined for the presence or absence of delay. Hopf bifurcation’s triggering circumstance is identified. Using the center manifold theorem and the normal form, the direction and stability of the bifurcating Hopf bifurcation are explored. The next step is sensitivity analysis, which explains the set of control settings that have an impact on how the system behaves. Finally, to further comprehend the model’s dynamical behavior and validate the discovered analytical conclusions, numerical simulation has been used.

show abstract

Asymptotic behavior of a stochastic SIR model with general incidence rate and nonlinear Lévy jumps

2022

View full text Add to dashboard Cite

In this paper, we consider a stochastic SIR epidemic model with general disease incidence rate and perturbation caused by nonlinear white noise and L vy jumps. First of all, we study the existence and uniqueness of the global positive solution of the model. Then, we establish a threshold by investigating the one-dimensional model to determine the extinction and persistence of the disease. To verify the model has an ergodic stationary distribution, we adopt a new method which can obtain the sufficient and almost necessary conditions for the extinction and persistence of the disease. Finally, some numerical simulations are carried out to illustrate our theoretical results.

show abstract

Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay

Cited by 9 publications

References 34 publications

Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

Dynamics Analysis of a Delayed Crimean‐Congo Hemorrhagic Fever Virus Model in Humans

Asymptotic behavior of a stochastic SIR model with general incidence rate and nonlinear Lévy jumps

Contact Info

Product

Resources

About