VIRAL MUTATIONS AS A POSSIBLE MECHANISM OF HIDDEN IMMUNIZATION AND CONTAINMENT OF A PANDEMIA

Juri Dimaschko; Victor Podolsky

Later on, the number of sick people increases until a significant majority of the population passes through the stage of the disease and thereby acquires immunity. At the beginning of the epidemic, the vast majority of people S(0) = 1 − I 0 are healthy I(0) = I 0 1 is the initial fraction of carriers of the virus, R(0) = 0 -nobody have been sick and gained immunity so far). During the epidemic, a significant fraction of people 0 < I (t) < 1are sick. At the end of the epidemic, there are no more sick people, I(t) = 0. Some people R(t) as a result of the epidemic went through disease and gain immunity, another part S(t) escaped the disease. The typical course of the epidemic in the SIR model is as follows (Fig.1) : The maximum fraction of the sick people during the epidemic is given by the relation [1] I max = 1 − (1 + ln r) /r (4) It follows from this that the fraction of sick people at the peak of the epidemic can be very high. So, at r = 5 it is I max = 48% as shows the I(t) plot in Fig.1 . Experience shows that the fraction of sick people never reaches this level. This fact alone indicates the incompleteness of the SIR model and the existence of other mechanisms for ending the epidemic, not related to the acquisition of immunity by people through the stage of the disease.