Modeling TB-HIV syndemic and treatment

Tuberculosis (TB) and human immunodeficiency virus (HIV) can be considered a deadly human syndemic. In this article, we formulate a model for TB and HIV transmission dynamics. The model considers both TB and acquired immune deficiency syndrome (AIDS) treatment for individuals with only one of the infectious diseases or both. The basic reproduction number and equilibrium points are determined and stability is analyzed. Through simulations, we show that TB treatment for individuals with only TB infection reduces the number of individuals that become co-infected with TB and HIV/AIDS, and reduces the diseases (TB and AIDS) induced deaths. Analogously, the treatment of individuals with only AIDS also reduces the number of co-infected individuals. Further, TB-treatment for co-infected individuals in the active and latent stage of TB disease, implies a decrease of the number of individuals that passes from HIV-positive to AIDS.Comment: This is a preprint of a paper whose final and definite form is: Journal of Applied Mathematics (ISSN 1110-757X) 2014, Article ID 248407, http://dx.doi.org/10.1155/2014/24840

Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem

We consider a recent coinfection model for Tuberculosis (TB), Human Immunodeficiency Virus (HIV) infection and Acquired Immunodeficiency Syndrome (AIDS) proposed in [Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639--4663]. We introduce and analyze a multiobjective formulation of an optimal control problem, where the two conflicting objectives are: minimization of the number of HIV infected individuals with AIDS clinical symptoms and coinfected with AIDS and active TB; and costs related to prevention and treatment of HIV and/or TB measures. The proposed approach eliminates some limitations of previous works. The results of the numerical study provide comprehensive insights about the optimal treatment policies and the population dynamics resulting from their implementation. Some nonintuitive conclusions are drawn. Overall, the simulation results demonstrate the usefulness and validity of the proposed approach.Comment: This is a preprint of a paper whose final and definite form is with 'Computational and Applied Mathematics', ISSN 0101-8205 (print), ISSN 1807-0302 (electronic). Submitted 04-Feb-2016; revised 11-June-2016 and 02-Sept-2016; accepted for publication 15-March-201

A stochastic SICA epidemic model for HIV transmission

We propose a stochastic SICA epidemic model for HIV transmission, described by stochastic ordinary differential equations, and discuss its perturbation by environmental white noise. Existence and uniqueness of the global positive solution to the stochastic HIV system is proven, and conditions under which extinction and persistence in mean hold, are given. The theoretical results are illustrated via numerical simulations.Comment: This is a preprint of a paper whose final and definite form is with 'Applied Mathematics Letters', ISSN 0893-9659. Submitted 22/Jan/2018; Revised 03/May/2018; Accepted for publication 03/May/201

A sufficient optimality condition for delayed state-linear optimal control problems

We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear optimal control problem to an equivalent non-delayed problem. This allows us to use a well-known theorem that ensures a sufficient optimality condition for non-delayed state-linear optimal control problems. An example is given in order to illustrate the obtained result.Comment: This is a preprint of a paper whose final and definite form is with 'Discrete and Continuous Dynamical Systems -- Series B' (DCDS-B), ISSN 1531-3492, eISSN 1553-524X, available at [http://www.aimsciences.org/journal/1531-3492]. Paper Submitted 31/Dec/2017; Revised 13/April/2018; Accepted 11/Jan/201

Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil

We propose a new mathematical model for the spread of Zika virus. Special attention is paid to the transmission of microcephaly. Numerical simulations show the accuracy of the model with respect to the Zika outbreak occurred in Brazil.Comment: This is a preprint of a paper whose final and definite form is with 'Mathematical Methods in the Applied Sciences', ISSN 0170-4214. Submitted Aug 10, 2017; Revised Nov 13, 2017; accepted for publication Nov 14, 201

Ebola Model and Optimal Control with Vaccination Constraints

The Ebola virus disease is a severe viral haemorrhagic fever syndrome caused by Ebola virus. This disease is transmitted by direct contact with the body fluids of an infected person and objects contaminated with virus or infected animals, with a death rate close to 90% in humans. Recently, some mathematical models have been presented to analyse the spread of the 2014 Ebola outbreak in West Africa. In this paper, we introduce vaccination of the susceptible population with the aim of controlling the spread of the disease and analyse two optimal control problems related with the transmission of Ebola disease with vaccination. Firstly, we consider the case where the total number of available vaccines in a fixed period of time is limited. Secondly, we analyse the situation where there is a limited supply of vaccines at each instant of time for a fixed interval of time. The optimal control problems have been solved analytically. Finally, we have performed a number of numerical simulations in order to compare the models with vaccination and the model without vaccination, which has recently been shown to fit the real data. Three vaccination scenarios have been considered for our numerical simulations, namely: unlimited supply of vaccines; limited total number of vaccines; and limited supply of vaccines at each instant of time.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Industrial and Management Optimization' (JIMO), ISSN 1547-5816 (print), ISSN 1553-166X (online). Submitted February 2016; revised November 2016; accepted for publication March 201