Two viruses competition in the SIR model of epidemic spread: application to COVID-19

Abstract

The SIR model of the epidemic spread is used for consideration the problem of the competition of two viruses having different contagiousness. It is shown how the more contagious strain replaces over time the less contagious one. In particular the results can be applied to the current situation when the omicron strain appeared in population affected by the delta strain.

Strain-stream model of epidemic spread in application to COVID-19

“…1. This property, mentioned in [18], is valid also for the strain-stream model under consideration. In this paper, we are interested in the impact of a possible infection with virus 2 after recovery from an infection caused by virus 1.…”

“…As was revealed in [18] for γ 2 = 0, using the example of specific initial conditions and parameters p i and T i , the coexistence of two viruses of different contagiousness leads over time to the replacement of the less contagious strain by a more contagious one, even if the share of the latter at the beginning of the process was significantly smaller than less contagious. The results of calculations for specific parameters that correspond to the simultaneous emergence of an epidemic with two strains of different contagiousness are shown in Fig.…”

“…This situation corresponds to the epidemic process observed with the appearance of the omicron strain. An important difference from the specific examples considered in [18] is the appearance of strain 2 under conditions of a developed epidemic of strain 1, which is characterized by rather large initial values of u (0) and y 1 (0).…”

“…Here we use the same notations as in [18]. The value u ( t ) ≡ 1 − z ( t ) is the fraction of the population that is not affected by virus at all, z ( t ) = N tot ( t ) /N corresponds to the fraction of full population N that are affected (ill and recovered N tot ( t ) ≡ N 1 ( t ) + N 2 ( t )) by the strain 1 ( N 1 ) or the strain 2 ( N 2 ) to the time t .…”

“…The more 0 ≡ γ 2 ≡ 1, the faster the process of infection with strain 1 is suppressed, i.e. it is forced out faster than in the original model with γ 2 = 0 [18] (see also Fig. 1).…”