An optimal control problem applied to malaria disease in Colombia

Abstract

In Colombia, malaria is a public health problem that affects a large part of its population. Above motivated us to formulate an optimal control problem considering the following control variables: bed nets (BN), intermittent prophylactic treatment in pregnancy (IPTp) and prompt and effective case management (PECM). The results reveal the importance of congenital transmission and death due to disease in the infection outcome. It is imperative that strategies be defined to reduce these risk factors.

A stability test for non linear systems of ordinary differential equations based on the Gershgorin circles

“…The test can be used to verify the equilibrium solution of different models such as those developed in [4,5,6,7,8,9,10,11,12,13,14,15,16,17]. However, in this section we will analyze the stability of the SEIR model, a multi-patch model and a model on immunology of tuberculosis.…”

Analyzing the impact of the media campaign and rapid testing for COVID-19 as an optimal control problem in East Java, Indonesia

“…By definition, given the control set Γ, where u i ∈ [0, 1] 2 for then we have Γ is closed. Using the definition of convex set (Proposition 2.4 in [48] ), for any arbitrary points y and z in Γ, where we have that Thus, implying Γ is convex. The time-dependent control model in (11) is linear in control variables u 1 and u 2 with coefficients depending on the state variables S u and A .…”

Modelo multiparche y multigrupo para la transmisión de la malaria

“…Además, la distribución espacial que tiene la población y el hecho de que en la literatura se puede encontrar diversos modelos en ecuaciones diferenciales ordinarias para la dinámica de la malaria, donde se considera que la población esta distribuida homogéneamente sin considerar la movilidad ni los grupos [15,16,17,18,19,20,21], propicia la idea de estudiar el efecto de estos aspectos en un modelo clásico como el de Ross-Macdonald. Una base fundamental para formular el modelo se encuentra desarrollada en el artículo [22], en el cual proponen un modelo multiparche y multigrupo para la dinámica SEIRS.…”