In this work we develop a new Reservoir-People (RP) transmission network model to simulate the potential transmission of the COVID-19 virus in the population of Morocco. Our model is original in the sense that it contains parameters that depend on the confinement phases that Morocco has adopted so far. After developing the mathematical model COVID-19-Morocco we define a cost function to minimize with respect to the parameters. We then use genetic algorithms to optimize this functional. The numerical results we obtain confirm that our model is robust and can predict the evolution of the virus in Morocco.
This work proposes a novel nonlinear parabolic equation with p(x)-growth
conditions for image restoration and enhancement. Based on the
generalized Lebesgue and Sobolev spaces with variable exponent, we
demonstrate the well-posedness of the proposed model. As a first result,
we prove the existence of a weak solution to our model when the reaction
term is bounded by a suitable function. Secondly, we use the
approximations method to establish the existence of a nonnegative weak
SOLA solution (Solution Obtained as Limit of Approximations) to the
proposed model. Finally, numerical experiments illustrate that the
proposed model performs better for image enhancement and denoising.
We develop a new technique to mathematically analyze and numerically simulate
the weak periodic solution to a class of semilinear periodic parabolic
equations with discontinuous coefficients. We reformulate our problem into a
minimization problem via a least-squares cost function. By using variational
calculus theory, we establish the existence of an optimal solution and based
on the Lagrangian method, we calculate the derivative of our cost function.
To illustrate the validity and efficiency of our proposed method, we present
some numerical examples with different periods of time and diverse choices
of discontinuous coefficients.
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