An incidence curve of acute respiratory infections in Moscow hasthree picks between September and April and reaches its maximum in January-February. The emergence of new strains of influenza A could account for onlyone pick a year. The most cases of common cold are caused by ubiquitous lowpathogenic viruses. In order to simulate weekly fluctuation of incidence rate ofacute respiratory illnesses we developed an agent-based model. It contains 10 millions agents with such attributes as sex, age, social status, levels of specific immune memory and lists of contacts. Each agent can contact with members of its household, colleagues or classmates. Through such contacts susceptible agent can be infected with one of seven circulating respiratory viruses. Viruses differ in their immunologic properties and assume to present influenza A virus, influenza B virus, parainfluenza, adenovirus, coronavirus, rhinovirus and respiratory syncytial virus. The rate of transmission depends on duration of contact, vulnerability of susceptible agent, infectivity of infected agent and air temperature. Proposed network of social interactions proved to be sufficiently detailed as it provided good fitting for observed incidence rate including periods of school holidays and winter public holidays. Additionally, the estimates of basic reproductive rate for the viruses confirm that all these viruses except new strains of influenza A are relatively harmless and unable to cause significant growth of acute respiratory infections morbidity.