DOS SANTOS, Fernando Luiz Pio; BENDAHMANE, Mostafa; ERRAJI, Elmahdi; KARAMI, Fahd

doi:10.1142/S0218339023300026

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DOS SANTOS, Fernando Luiz Pio
Universidade Estadual Paulista Júlio de Mesquita Filho = São Paulo State University [UNESP]

BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
IHU-LIRYC

ERRAJI, Elmahdi
Ecole Supérieure de Technologie d'Essaouira

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Journal of Biological Systems. 2023-06-13, vol. 31, n° 02, p. 345-373

World Scientific Publishing

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In this paper, we developed an optimal control of a reaction–diffusion mathematical model, describing the spatial spread of dengue infection. Compartments for human and vector populations are considered in the model, including a compartment for the aquatic phase of mosquitoes. This enabled us to discuss the vertical transmission effects on the spread of the disease in a two-dimensional domain, using demographic data for different scenarios. The model was analyzed, establishing the existence and convergence of the weak solution for the model. The convergence of the numerical scheme to the weak solution was proved. For numerical approximation, we adopted the finite element scheme to solve direct and adjoint state systems. We also used the nonlinear gradient descent method to solve the optimal control problem, where the optimal management of government investment was proposed and leads to more effective dengue fever infection control. These results may help us understand the complex dynamics driven by dengue and assess the public health policies in the control of the disease.< Réduire

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Epidemic Model

Reaction-Diffusion System

Aedes

Optimal Control

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A continuous spatial and temporal mathematical model for assessing the distribution of dengue in Brazil with control

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