Fractional order epidemiological model of SARS-CoV-2 dynamism involving Alzheimer's disease

Abstract

In this paper, we study a Caputo-Fabrizio fractional order epidemiological model for the transmission dynamism of the severe acute respiratory syndrome coronavirus 2 pandemic and its relationship with Alzheimer's disease. Alzheimer's disease is incorporated into the model by evaluating its relevance to the quarantine strategy. We use functional techniques to demonstrate the proposed model stability under the Ulam-Hyres condition. The Adams-Bashforth method is used to determine the numerical solution for our proposed model. According to our numerical results, we notice that an increase in the quarantine parameter has minimal effect on the Alzheimer's disease compartment.

Keywords: Alzheimer’s disease; Caputo–Fabrizio fractional derivatives; Numerical scheme; SARS-CoV-2 pandemic; Ulam–Hyres stability.

Fig. 1

Numerical trajectory of the CF-fractional order derivative, ${\mu }_{\ast }$ of the model (2).

Fig. 2

Numerical trajectory of the CF-fractional order derivative, ${\mu }_{\ast }$ of the model (2).

Fig. 3

Dynamics of individuals who have had a Alzheimer’s disease over time under different ${\gamma }_1$ (left) and ${\gamma }_2$ (right).

Fig. 4

Numerical trajectory of the Alzheimer’s disease over time under different values of $m$.

Fig. 5

Dynamics of individuals who have had a Alzheimer’s disease over time under different ${\xi }_1$ (left) and ${\xi }_2$ (right).