Modelo para la transmisión del VIH en una población con diferenciación de sexos y usos de medidas preventivas

Abstract

En este artículo se formula un modelo basado en ecuaciones diferenciales ordinarias, para describir la dinámica de transmisión del VIH considerando una diferenciación en la población según el géneroy la orientación sexual, con el fin de analizar el impacto que el uso de medidas preventivas tiene en la reducción de la transmisión del virus. Se realiza además un estudio de simulación numérica para ilustrar diferentes escenarios de control mediante medidas preventivas.

Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation

“…A wide variety of mathematical models have been formulated to study HIV infection at the cellular level [2,3,18,20,21,23,24,26,28,[31][32][33][34][35]37,38,40,[46][47][48] as well as its spread in susceptible populations [7,10,22,39,44,45]. Such models approach the study of infection from different perspectives, and have made it possible to evaluate the effect that preventive measures or prophylaxis and diagnosis may have in reducing transmission [10,11,17,39,41,43], the effectiveness of antiretrovirals in controlling viral loads, in this case, optimal control models have been very important tools [20,23,31,[41][42][43][44]46]. Finally, any study must begin from the knowledge of the virus and how it interacts with the host's immune system, in particular, a more relevant topic is latent infection in people who are unaware of its serological status.…”

Aprendizaje de las ecuaciones diferenciales desde un enfoque cualitativo

“…Este tema es relevante desde tiempos de Newton, quien logró desarrollar el cálculo y -más importante aún-modeló las leyes de la mecánica clásica al valerse de las ecuaciones diferenciales (Abell & Braselton, 2014). Por lo tanto, desde su génesis, las ecuaciones diferenciales se convirtieron en un importante recurso para la modelación y solución de problemas (Bender, 1978;Toro, 2018).…”

Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation

“…A wide variety of mathematical models has been formulated to study HIV infection at cellular level [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], as well as its spread in uninfected populations [28][29][30][31][32][33]. Such models address the study of infection from different perspectives and have made it possible to evaluate the possible effect of preventive measures or prophylaxis and diagnosis on reducing transmission [29,31,[34][35][36][37]. Concerning the effectiveness of antiretroviral medications in controlling viral loads, optimal control models have been very important tools [11,13,17,25,32,[36][37][38].…”

“…Such models address the study of infection from different perspectives and have made it possible to evaluate the possible effect of preventive measures or prophylaxis and diagnosis on reducing transmission [29,31,[34][35][36][37]. Concerning the effectiveness of antiretroviral medications in controlling viral loads, optimal control models have been very important tools [11,13,17,25,32,[36][37][38]. Finally, any study must begin with knowledge of the virus and how it interacts with the host's immune system.…”