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

Spread and Control of the Dynamics of HIV/AIDS-TB Co-infection in Ethiopia: A Mathematical Model Analysis

In this work we considered a nonlinear deterministic dynamical system to study the dynamics of HIV/AIDS-TB co-infection in Ethiopia. We found the system exhibit disease free equilibrium point and endemic equilibrium point. For the reproduction number  the disease-free equilibrium point is locally asymptomatically stable and the endemic equilibrium point is locally asymptomatically unstable. We calculate basic reproduction number of the HIV/AIDS-TB co-infection dynamical system which depends on six parameters. Using real data collected from different sectors in Ethiopia we found that the numerical value of the basic reproduction number is. This shows that HIV/AIDS–TB co-infection spread in the society. Using sensitive analysis, we identify the most influential control parameter is the HIV/AIDS-TB co-infection transmission rate. The HIV/AIDS-TB co-infection transmission rate which numerical value to be 0.021. But the real value of is 0.74, to be 0.74 in to 0.021 by fixing the number of contacts for HIV/AIDS-TB co-infection we decrease the effective number of contacts for HIV/AIDS-TB co-infection 74 to 21.  We also perform numerical simulation based on real data collected from different health sectors in Ethiopia. &nbsp

Optimal control of hepatitis C antiviral treatment programme delivery for prevention amongst a population of injecting drug users.

In most developed countries, HCV is primarily transmitted by injecting drug users (IDUs). HCV antiviral treatment is effective, and deemed cost-effective for those with no re-infection risk. However, few active IDUs are currently treated. Previous modelling studies have shown antiviral treatment for active IDUs could reduce HCV prevalence, and there is emerging interest in developing targeted IDU treatment programmes. However, the optimal timing and scale-up of treatment is unknown, given the real-world constraints commonly existing for health programmes. We explore how the optimal programme is affected by a variety of policy objectives, budget constraints, and prevalence settings. We develop a model of HCV transmission and treatment amongst active IDUs, determine the optimal treatment programme strategy over 10 years for two baseline chronic HCV prevalence scenarios (30% and 45%), a range of maximum annual budgets (£50,000-300,000 per 1,000 IDUs), and a variety of objectives: minimising health service costs and health utility losses; minimising prevalence at 10 years; minimising health service costs and health utility losses with a final time prevalence target; minimising health service costs with a final time prevalence target but neglecting health utility losses. The largest programme allowed for a given budget is the programme which minimises both prevalence at 10 years, and HCV health utility loss and heath service costs, with higher budgets resulting in greater cost-effectiveness (measured by cost per QALY gained compared to no treatment). However, if the objective is to achieve a 20% relative prevalence reduction at 10 years, while minimising both health service costs and losses in health utility, the optimal treatment strategy is an immediate expansion of coverage over 5-8 years, and is less cost-effective. By contrast, if the objective is only to minimise costs to the health service while attaining the 20% prevalence reduction, the programme is deferred until the final years of the decade, and is the least cost-effective of the scenarios

Analysis, Simulation and Control of a New Measles Epidemic Model

In this paper the problem of modeling and controlling the measles epidemic spread is faced. A new model is proposed and analysed; besides the categories usually considered in measles modeling, the susceptible, the exposed, the infected, the removed and, less frequently, the quarantine individuals, two new categories are herein introduced: the immunosuppressed subjects, that can not be vaccinated, and the patients with an additional complication, not risky by itself but dangerous if caught togeter with the measles. These two novelties are taken into account in designing and scheduling suitably control actions such as vaccination, whenever possible, prevention, quarantine and treatment, when limited resources are available. An analysis of the model is developed and the optimal control strategies are compared with other not optimized actions. By using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection to immunosuppressed individuals, as well as the importance of a prompt response of the society when an epidemic spread occurs, such as the quarantine intervention

Mathematical modelling of internal HIV dynamics

We study a mathematical model for the viral dynamics of HIV in an infected individual in the presence of HAART. The paper starts with a literature review and then formulates the basic mathematical model. An expression for R0, the basic reproduction number of the virus under steady state application of HAART, is derived followed by an equilibrium and stability analysis. There is always a disease-free equilibrium (DFE) which is globally asymptotically stable for R0 1 then some simulations will die out whereas others will not. Stochastic simulations suggest that if R0 > 1 those which do not die out approach a stochastic quasi-equilibrium consisting of random uctuations about the non-trivial deterministic equilibrium levels, but the amplitude of these uctuations is so small that practically the system is at the non-trivial equilibrium. A brief discussion concludes the paper