Susceptibles and infecteds for an uncontrolled epidemic. The dotted horizontal line indicates the threshold level of susceptibles Sth below which population immunity prevents further outbreaks. The arrow indicates the difference between the number of susceptibles at the end of the outbreak and Sth. We term this difference the overshoot.
Here, overshoot refers to the standard property of epidemics in closed populations of peaking when they have reduced the number of susceptibles to a level that can no longer maintain growth of the epidemic (in simple models, to 1/R0), but continue to infect more as the epidemic declines, so that the proportion of the population that escapes infection by the end of the epidemic is less than 1/R0. The precursor epidemic of the sensitive strain reduces this overshoot and thereby results in a smaller attack rate. This phenomenon is explained more generally and more quantitatively in Protocol S1.
suggests that when antivirals are the only mode of control, using antivirals towards the end of the epidemic to minimize overshoot is a good control policy.
It is seen that the vaccination decreases the overshoots compared to the vaccination-free case.
The excess number of infected people beyond those needed to reach the critical threshold level has been termed ‘overshoot’; an optimal intervention minimizes this overshoot and thereby minimizes the attack rate over all outbreaks. We have previously studied this scenario and it has also been recognized in the context of antiviral treatment of a drug sensitive influenza outbreak, followed by a drug resistant outbreak.
The second uses the time required for a major epidemic to take place, conditional on non-extinction in the short term, to quantify the delay effect, i.e., the difference in the timing of epidemic overshoot between scenarios in the presence and absence of selective travel restrictions.
Since the small outbreak in the former time period was restricted to a limited number of schools and the contacts made by the students in Osaka and Kobe (and as Japan was unique in successfully "containing" the local school-based outbreak before actual pandemic overshoot), the depletion of susceptibles in May and undiagnosed cases are unlikely to have played a significant role in our estimates of a smaller R for the epidemic in the latter transmission period, which saw the pandemic takeover.
A mitigated two-phase epidemic may result in a cumulative burden of morbidity and mortality less than that observed in a single unchecked epidemic because of reduced epidemic overshoot .
This can be explained by one of our previous studies, where we showed that the minimization of an “overshoot” – defined as the excess infections that occur during the waning phase of an outbreak – will lead to an optimal control strategy for multiple outbreaks, such as a drug sensitive outbreak followed by a drug resistant one.