Investigating the impact of nonlinearity on virus spread in computer networks with quarantine compartments

A new compartmental model was proposed by adding quarantine to the classic Susceptible–Infected–Removed (SIR) model, which allows machines to be repaired or removed through quarantine. Firstly, our new model, Susceptible–Infected–Quarantine–Removed (SIQR), evaluates how saturation and non-saturation between infected and quarantined machines affect the results, generating two scenarios. In the analysis, we calculated the local stability and equilibrium points. In the non-saturation model, there is only one equilibrium point with a transcritical bifurcation. These bifurcation conditions suggest that all machines can become susceptible or not. In the non-linear model, there are two equilibrium points, one of which is endemic. Numerical simulations corroborated the theoretical results. The introduction of quarantine compartments and non-linear relationships enhances the descriptive and predictive power of the model. Quarantine allows for the represent of automatic isolation and infection mitigation, while nonlinear interactions capture effects such as saturation in infection rates, critical thresholds, and dynamic behaviors. • Study of the introduction of computers in quarantine after infection as a virus mitigation strategy. • Study of the influence of nonlinearity between infected and quarantined machines. • Comparative study considering the presence and absence of nonlinearity between infected and quarantined machines.