An Inverse Problem for Delay Differential Equations: Parameter Estimation, Nonlinearity, Sensitivity

Rihan, Fathalla A.; Азамов, Абдулла; Alsakaji, Hebatallah J.

doi:10.18576/amis/120106

Cited by 19 publications

(17 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Incorporating time lags (or time delays) in biological models makes the systems much more realistic, as it can destabilize the equilibrium points and give rise to a stable limit cycle, causing oscillations to grow and enriching the dynamics of the model. Time delays have been considered and extremely studied by many authors in prey-predator models and biological systems (see [21][22][23][24][25]).…”

Section: Time Delaysmentioning

confidence: 99%

Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect

2020

View full text Add to dashboard Cite

Allee effect is one of the important factors in ecology, and taking it into account can cause significant impacts in the system dynamics. In this paper, we study the dynamics of a two-prey one-predator system, where the growth of both prey populations is subject to Allee effects, and there is a direct competition between the two-prey species having a common predator. Two discrete time delays τ 1 and τ 2 are incorporated into the model to represent reaction time of predators. Sufficient conditions for local stability of positive interior equilibrium and existence of Hopf bifurcations in terms of threshold parameters τ * 1 and τ * 2 are obtained. A Lyapunov functional is deducted to investigate the global stability of positive interior equilibrium. Sensitivity analysis to evaluate the uncertainty of the state variables to small changes in the Allee parameters is also investigated. Presence of Allee effect and time delays in the model increases the complexity of the model and enriches the dynamics of the system. Some numerical simulations are provided to illustrate the effectiveness of the theoretical results. e model is highly sensitive to small changes in Allee parameters at the early stages and with low population densities, and this sensitivity decreases with time.Hindawi Complexity Volume 2020, Article ID 7306412, 15 pages https://doi.

show abstract

Section: Time Delaysmentioning

confidence: 99%

Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect

2020

View full text Add to dashboard Cite

show abstract

“…We should also mention here that time-delays (time-lags) have been extensively introduced into equations used in mathematical ecology to represent the time required for maturation period, reaction time, feeding time, etc. [17][18][19]. The presence of time-delay in a system greatly affects its stability.…”

Section: Introductionmentioning

confidence: 99%

Persistence and extinction for stochastic delay differential model of prey predator system with hunting cooperation in predators

Rihan

Alsakaji

2020

Adv Differ Equ

Self Cite

View full text Add to dashboard Cite

Stochastic differential models provide an additional degree of realism compared to their corresponding deterministic counterparts because of the randomness and stochasticity of real life. In this work, we study the dynamics of a stochastic delay differential model for prey-predator system with hunting cooperation in predators. Existence and uniqueness of global positive solution and stochastically ultimate boundedness are investigated. Some sufficient conditions for persistence and extinction, using Lyapunov functional, are obtained. Illustrative examples and numerical simulations, using Milstein's scheme, are carried out to validate our analytical findings. It is observed that a small scale of white noise can promote the survival of both species; while large noises can lead to extinction of the predator population.

show abstract

“…We also mention here that there are many problems in biosciences (such as epidemics, harvesting, chemostat, treatment of diseases, physiological control, vaccination) which can be addressed within an optimal control framework for systems of DDEs [16][17][18][19]. However, the amount of real experience that exists with optimal control problems (OCPs) is still small.…”

Section: Introductionmentioning

confidence: 99%

Delay Differential Model for Tumour-Immune System With Chemo-therapy and Optimal Control

Rihan

2020

ITM Web Conf.

Self Cite

View full text Add to dashboard Cite

In this paper, we present a mathematical model of tumour-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. The control variables are included to justify the best strategy of treatments with minimum side effects, by reducing the production of new tumour cells and keeping the number of normal cells above the average of its carrying capacity. Existence of optimality and optimality conditions are also proved. The numerical simulations show that the optimal treatment strategy reduces the load of tumour cells and increases the effector cells after few days of therapy.

show abstract

An Inverse Problem for Delay Differential Equations: Parameter Estimation, Nonlinearity, Sensitivity

Cited by 19 publications

References 16 publications

Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect

Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect

Persistence and extinction for stochastic delay differential model of prey predator system with hunting cooperation in predators

Delay Differential Model for Tumour-Immune System With Chemo-therapy and Optimal Control

Contact Info

Product

Resources

About