HIV–TB co-infection treatment: Modeling and optimal control theory perspectives

Abstract

An important question, of whether the initiation of HIV treatment during ongoing TB treatment for HIV-TB co-infected individuals is appropriate, still remains unanswered; initiating HIV treatment at or soon after the start of the TB treatment course has some advantages including fewer HIV-related deaths and a lower risk of HIV transmission as well as some disadvantages including occurrence of Immune Reconstitution Inflammatory Syndrome (IRIS) due to a high pill burden. In this study, we develop a mathematical model to explore the effects of early and late HIV treatment, during the TB treatment course, on new HIV infections, HIV-related deaths, and IRIS cases. Mathematical analyses of our model indicate that co-infection treatment programs alone cannot eradicate the diseases; additional interventions and/or treatments targeting individuals infected with a single disease are necessary for successful disease eradication. Numerical computations of the model solution demonstrate that outcomes of the treatment programs aiming to reduce the total burden of this co-infection depend highly on both the strength and initiation timing of antiretroviral therapy (ART). Based on our model, we also formulate an optimal control problem and solve it using Pontryagin's Maximum Principle and an efficient numerical iterative method. Our numerical results of an optimal HIV-TB treatment protocol that yields a minimum burden from this co-infection indicates that each of the new HIV infections, HIV-related deaths and IRIS cases is important for achieving optimal benefits from the co-infection treatment programs.

A fractional order HIV‐TB coinfection model with nonsingular Mittag‐Leffler Law

“…The figures obtained show same numerical simulations to those generated by standard HIV‐TB coinfection model for the integer order. In the classical case , the results obtained are in agreement with those obtained by Mallela et al and suggest that our fractional model is well posed.…”

“…The sexual partners by , the users of prophylactics are , the unprotected intimate partners who transmit the disease to a susceptible with a relation . The unprotected coinfected personals (in the compartment) enter the compartment with the TB treatment as suggested in Mallela et al. Initiating HIV treatment with the TB treatment development has some advantages including less HIV‐related losses and an inferior risk of HIV spread also having difficulties including incidence of immune reconstitution inflammatory syndrome (IRIS) because of large pills encumbrance.…”

“…Pinto and Carvalho considered a coinfected HIV and TB model in the resistance of multidrugs for the global stability and numerical simulations. Mallela et al proposed an HIV‐TB coinfected model for the mathematical analysis, and they established numerical study of their model for different aspects of the model. Silva and Torres proposed a fractional order model for HIV/AIDS transmission, and the local and uniform stability of the model were studied.…”

Optimal control of HIV resistance and tuberculosis co-infection using treatment intervention

“…Many researchers have modeled the dynamics of HIV and TB co-infection [4][5][6]. For instance, Mallela et al [4] developed a novel mathematical model that evaluates treatment strategies for HIV and TB co-infected individuals.…”

“…Many researchers have modeled the dynamics of HIV and TB co-infection [4][5][6]. For instance, Mallela et al [4] developed a novel mathematical model that evaluates treatment strategies for HIV and TB co-infected individuals. A research [5] proposed a mathematical model to study the dynamic of TB for the spread of HIV in a logistically-growing population.…”