arXiv subjects

Khalid Hattaf

Publications and source records attributed to Khalid Hattaf.

2 recordsLinked to original sources

arXiv2020

Modeling the spread of COVID-19 pandemic in Morocco

Nowadays, coronavirus disease 2019 (COVID-19) poses a great threat to public health and economy worldwide. Unfortunately, there is yet no effective drug for this disease. For this, several countries have adopted multiple preventive interventions to avoid the spread of COVID-19. Here, we propose a delayed mathematical model to predict the epidemiological trend of COVID-19 in Morocco. Parameter estimation and sensitivity analysis of the proposed model are rigorously studied. Moreover, numerical simulations are presented in order to test the effectiveness of the preventive measures and strategies that were imposed by the Moroccan authorities and also help policy makers and public health administration to develop such strategies.

q-bio.PE↗

arXiv2020

Lyapunov functions for fractional-order systems in biology: methods and applications

We prove new estimates of the Caputo derivative of order $α\in (0,1]$ for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a fractional cellular model are studied. More precisely, we construct suitable Lyapunov functionals to demonstrate the global stability of the free and endemic equilibriums, for both fractional models, and we also perform some numerical simulations that confirm our choices.

math.OC↗