A memory effect model to predict COVID-19: analysis and simulation

Ali, Aatif; Hamou, Abdelouahed Alla; Islam, Saeed; Muhammad, Taseer; Khan, Alamzeb

doi:10.1080/10255842.2022.2081503

Cited by 11 publications

(2 citation statements)

References 33 publications

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“…According to our study, the obtained approximation after only one iteration is considered very good. The results obtained by OAFM for system of integral equations are compared with Biorthogonal systems in a Banach space Fixed point, the implicit Trapezoidal rule in conjunction with Newton's method, RMCM in the form of tables and figures (See 12) According to the numerical results which obtaining from the illustrative examples, we conclude that our method is more powerful for the solution convergence than the other methods and can be applied for more physical like [36,37,38,39] in future.…”

Section: Discussionmentioning

confidence: 96%

Theory and Computations for the System of Integral Equations via the use of Optimal Auxiliary Function Method

Zada¹,

Naz²,

Nawaz³

2022

IJEMD-M

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This paper extends the application of Optimal Auxiliary Function Method (OAFM) to the system of integral equations. The system of Volterra integral equations of second kind are taken as test examples. The results obtained by proposed method are compared with different methods i.e., Biorthogonal systems in a Banach space Fixed point, the implicit Trapezoidal rule in conjunction with Newton's method, and Relaxed Monte Carlo method (RMCM). The results revealed that OAFM is more efficient, simple to apply, and fast convergent. The auxiliary functions used in the method control its convergence. The values of arbitrary constants involved in the auxiliary functions are calculated optimally using the method of least square

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Section: Discussionmentioning

confidence: 96%

Theory and Computations for the System of Integral Equations via the use of Optimal Auxiliary Function Method

Zada¹,

Naz²,

Nawaz³

2022

IJEMD-M

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“…To study the impact of advection on the schistosomiasis spread, similar to the numerical method found in Aatif et al. ( 2023 ), we examine the influence of the advection rates and on the value of in Fig. 4 a and b, respectively.…”

Section: Numerical Simulationmentioning

confidence: 99%

Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Wu,

Salmaniw,

Wang

2024

J. Math. Biol.

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Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number $${\mathcal {R}}_0$$ R 0 and show that the disease-free periodic solution is globally attractive when $${\mathcal {R}}_0<1$$ R 0 < 1 whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when $${\mathcal {R}}_0>1$$ R 0 > 1 . Moreover, we find that $${\mathcal {R}}_0$$ R 0 is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

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Memory effects in disease modelling through kernel estimates with oscillatory time history

Mielke,

Sørensen,

Wyller

2024

J. Math. Biol.

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We design a linear chain trick algorithm for dynamical systems for which we have oscillatory time histories in the distributed time delay. We make use of this algorithmic framework to analyse memory effects in disease evolution in a population. The modelling is based on a susceptible-infected-recovered SIR—model and on a susceptible-exposed-infected-recovered SEIR—model through a kernel that dampens the activity based on the recent history of infectious individuals. This corresponds to adaptive behavior in the population or through governmental non-pharmaceutical interventions. We use the linear chain trick to show that such a model may be written in a Markovian way, and we analyze the stability of the system. We find that the adaptive behavior gives rise to either a stable equilibrium point or a stable limit cycle for a close to constant number of susceptibles, i.e. locally in time. We also show that the attack rate for this model is lower than it would be without the dampening, although the adaptive behavior disappears as time goes to infinity and the number of infected goes to zero.

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A memory effect model to predict COVID-19: analysis and simulation

Cited by 11 publications

References 33 publications

Theory and Computations for the System of Integral Equations via the use of Optimal Auxiliary Function Method

Theory and Computations for the System of Integral Equations via the use of Optimal Auxiliary Function Method

Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Memory effects in disease modelling through kernel estimates with oscillatory time history

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