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Abstract Mathematical models of viral dynamics in vivo provide incredible insights into the mechanisms for the nonlinear interaction between virus and host cell populations, the dynamics of viral drug resistance, and the way to eliminate virus infection from individual patients by drug treatment. The integration of these mathematical models with high-throughput genetic and genomic data within a statistical framework will raise a hope for effective treatment of infections with HIV virus through developing potent antiviral drugs based on individual patients’ genetic makeup. In this opinion article, we will show a conceptual model for mapping and dictating a comprehensive picture of genetic control mechanisms for viral dynamics through incorporating a group of differential equations that quantify the emergent properties of a system.

Abstract Background Despite our increasing recognition of the mechanisms that specify and propagate epigenetic states of gene expression, the pattern of how epigenetic modifications contribute to the overall genetic variation of a phenotypic trait remains largely elusive. Results We construct a quantitative model to explore the effect of epigenetic modifications that occur at specific rates on the genome. This model, derived from, but beyond, the traditional quantitative genetic theory that is founded on Mendel’s laws, allows questions concerning the prevalence and importance of epigenetic variation to be incorporated and addressed. Conclusions It provides a new avenue for bringing chromatin inheritance into the realm of complex traits, facilitating our understanding of the means by which phenotypic variation is generated.