The local stability of a modified multi-strain SIR model for emerging viral strains

Miguel Fudolig; Reka Howard

More recently, the anti-vaccination movement has been gaining traction in different 2 parts of the world. Individuals who do not advocate vaccination commonly cite reasons 3 such as fear of adverse side-effects, perceived low efficacy of vaccines, and perceived low influenza-like illness in Israel accounting for weather and antigenic drift by adding terms 48 that account for weather signals and lost of immunity. Finkenstadt et al. [31] created a 49 predictive stochastic SIRS model for weekly flu incidence accounting for antigenic drift. 50 Roche et al. [32] used an agent-based SIR model to describe the spread of a multi-strain 51 epidemic, while Shi et al. [33] used the same approach and empirical data from Georgia, 52 USA to model an influenza pandemic that incorporates viral mutation and seasonality. 53 However, these approaches have been stochastic in nature, which does not provide 54 information regarding the stability and existence of equilibrium points in an infected 55 population. The abovementioned articles also do not take vaccination and the presence 56 of other strains into account in their models. Consequently, one can model the presence 57 of a mutated virus spreading into a population using a multi-strain model, which was 58 used in the following studies for avian flu [23, 24] . These models study the birds and the 59 humans as one population in an SI-SIR model, where the first SI corresponds to the 60 compartments for the avian species. However, the two infected compartments in this 61 model do not cross since they are separated by species. Casagrandi et al. [25] 62 introduced a non-linear deterministic SIRC epidemic model to model the influenza A 63 virus undergoing an antigenic drift. The SIRC model is a modified SIR model with an 64 additional compartment, C, for individuals that receive partial immunity from being which did not investigate the equilibrium model in detail.