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$\textbf{Background:}$ High mutability of HIV is the driving force ofantiretroviral drug resistance, which represents a medical care challenge.  $\textbf{Method and Model Equation:}$ To detect the mutability of each genein the HIV-1 genome; a mathematical analysis of HIV-1 genome is performed,depending on a linear relation wherein the probability of spontaneous mutationsemergence is directly proportional to the ratio of the gene length to the wholegenome length. \begin{equation*} {P_g}{S_i} =\frac{g}{G} \end{equation*}  $\textbf{Results:}$ $\textbf{tat}$, $\textbf{vpr}$ and $\textbf{vpu}$ are theleast mutant genes in HIV-1 genome. Protease $\textbf{PROT}$ gene is the leastmutant gene component of the polymerases $\textbf{pol}$.  $\textbf{Conclusion:}$ $\textbf{tat}$, $\textbf{vpr}$ and $\textbf{vpu}$ arethe best candidates for HIV-1 recombinant subunit vaccines or as a part of$\textit{prime and boost}$ vaccine combinations. Also; the proteaseinhibitor-based regime represents a high genetic barrier for HIV to overcome.

advances in microbiology

Mathematical Analysis of the Probability of Spontaneous Mutations in  HIV-1 Genome and Their Role in the Emergence of Resistance to Anti-Retroviral  Therapy