Infant deaths and old age deaths are very different. The former are mostly due to severe congenital malformations of one or a small number of specific organs. On the contrary, old age deaths are largely the outcome of a long process of deterioration which starts in the 20s and affects almost all organs. In terms of age-specific death rates, there is also a clear distinction: the infant death rate falls off with age, whereas the adult and old age death rate increases exponentially with age in conformity with Gompertz's law. An additional difference is that whereas aging and old age death have been extensively studied, infant death received much less attention. To our knowledge, the two effects have never been inter-connected. Clearly, it would be satisfactory to explain the two phenomena as being two variants within the same explanatory framework. In other words, a mechanism providing a combined explanation for the two forms of mortality would be welcome. This is the purpose of the present paper. We show here that the same biological effects can account for the two cases provided there is a difference in their severity: death triggered by isolated lethal anomalies in one case and widespread wear-out anomalies in the second. We show that quite generally this mechanism leads indeed, respectively, to a declining and an upgoing death rate. Moreover, this theoretical framework leads to the conjecture that the severity of the death effects, whether in infancy or old age, is higher for organisms which comprised a larger number of organs. Finally, let us observe that the main focus of the paper is the drastic difference of the age-specific death rates (i.e., decreasing versus increasing) because this difference is found in many species, whereas the question of the best fit (e.g., Gompertz versus Weibull) is rather specific to human mortality.