The prognosis of infectious diseases is determined by host-pathogen interactions. Control of pathogens has been the central dogma of treating infectious diseases in modern medicine, but the pathogen-directed medicine is facing significant challenges, including a lack of effective antimicrobials for newly emerging pathogens, pathogen drug resistance, and drug side effects. Here, a mathematic equation (termed equation of host-pathogen interactions, HPI-Equation) is developed to dissect the key variables of host-pathogen interactions. It shows that control of pathogens does not necessarily lead to host recovery. Instead, a combination of promoting a host's power of self-healing and balancing immune responses provides the best benefit for host. Moreover, the HPI-Equation elucidates the scientific basis of traditional Chinese medicine (TCM), a host-based medicine that treats infectious diseases by promoting self-healing power and balancing immune responses. The importance of self-healing power elucidated in the HPI-Equation is confirmed by recent studies that the tolerance mechanism, which is discovered in plants and animals and conceptually similar to self-healing power, improves host survival without directly attacking pathogens. In summary, the HPI-Equation describes host-pathogen interactions with mathematical logic and precision; it translates the ancient wisdoms of TCM into apprehensible modern sciences and opens a new venue for integrating TCM and modern medicine for a future medicine.

Key words: Host-pathogen interactions, HPI-Equation, Pathogen-targeted medicine, Host-based medicine, Traditional Chinese medicine, Self-healing power, Immune response, Tolerance