Optimal treatment strategies to control acute HIV infection

Abstract

Various antiretroviral therapies (ART) are administered to symptomatic human immunodeficiency virus (HIV) infected individuals to improve their health. The treatment effectiveness may depend on suppressing development of drug resistance, reduce evolution of new viral strains, minimize serious side effects and the costs of drugs. This paper deals with some results concerning optimal drug administration scheme successful in improving patients' health especially in poorly resourced settings. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, and the free viruses. Generally, in viral infection, the drug strategy aspects either the virus infectivity or reduce the virion production. The mathematical model proposed here, deals with both situations with the objective function based on a combination of maximizing benefit relied on T cells count (the white cells that coordinate activities of the immune system) and minimizing the systemic cost. The existence of the optimal control pair is established and the Pontryagin's minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward sweep method (FBSM). Our results indicate that early initiation of treatment makes a profound impact in both improving the quality of life and reducing the economic costs of therapy.

Optimal therapy for HIV infection containment and virions inhibition

“…Without referring to specific drugs or active principles, according to literature, as in ( Zephyr et al., 2021 ), ( Ahemd et al., 2021 ) and ( Agosto et al., 2014 ), there are different mechanisms known to the authors for the virus fight and the infection containment. One is represented by the Reverse Transcriptase Inhibitors , antiretroviral drugs that inhibit activity of viral DNA polymerase required for retrovirus replication, acting on the DNA chain construction and then limiting the virus replication.…”

Lyapunov Mappings and Analysis of a Nonlinear Spatio-temporal Epidemic Model

“…The present study and analysis may help to forecast and predict the probable treatment strategies. It is also interesting to extend this study to a vaccination model against malignant diseases [22][23][24][25][26][27][28][29] . The bifurcation analysis and chaos theory analysis in this model are another open problem for future studies [30] .…”