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 .
We propose a tractable epidemic model that includes containment measures. In the absence of containment measures , the epidemics spread exponentially fast whenever the infectivity rate is positive, \lambda>0. The containment measures are modeled by considering a time-dependent modulation of the bare infectivity \lambda leading to effective infectivity that decays in time for each infected individual, mimicking for instance the combined effect of the asymptomatic onset of the disease, testing policies and quarantine. We consider a wide range of temporal kernels for 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 newly infected individuals. We also propose a pandemic model caused by a growing number of separated foci .
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Susceptible-Infected (SI) epidemic spreading model including
tractable epidemic model that includes
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the
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the epidemics spreads exponentially fast for any value of the infectivity
, the epidemics spread exponentially fast whenever the infectivity rate is positive,
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an
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the
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the
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new
newly
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model with pandemic
pandemic model
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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
separated foci