Epidemics with containment measures

Bianconi, Ginestra; Krapivsky, Pavel L.

We propose a Susceptible-Infected (SI) epidemic spreading model including containment measures. In absence of containment measures the epidemics spreads exponentially fast for any value of the infectivity $\lambda>0$. The containment measures are modeled by considering a time-dependent modulation of the bare infectivity $\lambda$ leading to an effective infectivity that decays in time for each infected individual, mimicking for instance the combined effect of asymptomatic onset of the disease, testing policies and quarantine. We consider a wide range of temporal kernels for the effective infectivity and we investigate the effect of the considered containment measures. We find that not all kernels are able to push the epidemic dynamics below the epidemic threshold, with some containment measures only able to reduce the rate of the exponential growth of new infected individuals. We also propose a model with pandemic caused by a growing number of new separated foci. This model provides a stylized mathematical framework that can shed light on the role of different containment measures in mitigating and suppressing the spread of an epidemics such as COVID-19.