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HIV-1 affects tens of millions of people worldwide. Current treatments ofteninvolve a cocktail of antiretroviral drugs, which are effective in reducing thevirus and extending life spans. However, there is currently no FDA-approvedHIV-1 transcription inhibitor. Furthermore, there have only been a few attemptsto model the transcription process in HIV-1. In this work, we extend a novelthree-state model of HIV-1 transcription introduced in DeMarino et al. (2020)that has been developed and validated against experimental data. After fittingthis model to in vitro data, significant differences in the transcriptionprocess of HIV-1 in T-cells and macrophages have been observed. In particular,the activation of the HIV-1 promoter in T-cells appears to take place rapidlyas the Tat protein approaches a critical threshold. In contrast, the sameprocess occurs smoother in macrophages.  In this work, we carry out systematic mathematical analyses of the model tocomplement experimental data fitting and sensitivity analysis performedearlier. We derive explicit solutions of the model to obtain exacttranscription process decay rates for the original model and then study theeffect of nonlinearity on the system behavior, including the existence and thelocal and global stability of the positive equilibrium. We were able to showthe stability of the positive steady state in limiting cases, with the globalstability in the general case remaining an open question.  By modeling the effect of transcription-inhibiting drug therapy, we provide anontrivial condition for it to be effective in reducing viral load. Moreover,our numerical simulations and analysis point out that the effect of thetranscription-inhibitor can be enhanced by synchronizing with standardtreatments, such as combination antiretroviral therapy, to allow the reductionof total dosages and toxicity.

Mathematical analysis and potential therapeutic implications of a novel HIV-1 model of basal and activated transcription in T-cells and macrophages