introduction: The cause of the sudden infant death syndrome (SIDS) is perhaps the oldest of unsolved mysteries of medicine, possibly dating back to Exodus in Biblical times when Egyptian children died in their sleep as if from a plague. It occurs when infants die unexpectedly with no sufficient cause of death found in a forensic autopsy, including death scene investigation and review of medical history. That SIDS is an X-linked recessive death from infectious respiratory disease of a physiologically anemic infant and not a simple anomalous cardiac or neurological condition is an extraordinary claim that requires extraordinary evidence. If it were by a simple cause, it would have already been solved, with over 11,000 papers on SIDS listed now in PubMed. Our aim is to use mathematical models of SIDS to explain: (1) its 50% excess male death rate; (2) its 4-parameter lognormal distribution of ages at death; (3) its winter maxima and summer minima; and (4) its increasing rate with live-birth order.Methods: From extensive SIDS vital statistics data and published epidemiologic studies, we developed probability models to explain the mathematical behavior of SIDS meeting the four constraints mentioned above. We, then, compare these SIDS properties to infant death from acute respiratory infection (ARI), and infant death from encephalopathy, unspecified (EU).results: Comparisons show that SIDS are congruent with ARI and are not consistent with EU and that these probability models not only fit the SIDS data but they also predict and fit the male fraction of all infant and child mortality from birth through the first 5 years of their life.conclusion: SIDS are not rejected as an X-linked disease involving ARI and are not explained by a triple risk model that has been commonly accepted by the SIDS medical community, as implicating a neurological causation process in a subset of SIDS.