Modeling infectious disease: COVID-19 and beyond

In this talk, we introduce an age-structured epidemic model that recognizes waning and boosting of immune status of the host population. For some infectious diseases, as time evolves, the immunity of recovered individuals may be waining and reinfection could occur, but also their immune status could be boosted if they have contact with infective individuals. This is an important mechanism that makes the infectious disease control difficult. According to a classical malaria model by J. L. Aron, we incorporate a boosting mechanism expressed by the recovery-age into the SIRS epidemic model, where the immunity status is assumed to be determined by the recovery-age. We establish the condition for disease invasion and the existence of endemic steady states based on the basic reproduction number $R_0$. Subsequently, we determine the direction of bifurcation of endemic steady states bifurcated from the disease-free steady state, so we show that a backword bifurcation could exist under the waining and boosting of immune status.

The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has infected over 100 million cases and surpassed 2 million deaths to date. The ongoing pandemic has earned these grim milestones despite the extensive machinery developed to model and curtail outbreaks following the onset of the SARS epidemic almost 20 years ago. In part because of the high prevalence of milder cases and sub-notification created an ideal scenario for the spread of the disease. In this talk we will briefly discuss the basics of epidemic models and introduce a simple model based on the number of accumulated deaths that we developed at the beginning of the pandemic. The model shares a close connection with an approximate solution of the SIR model and allowed us to estimate epidemiological parameters. In particular, we calculate the basic reproduction number for the first wave of infections in France, followed by its rapid increase after the relaxation of the lockdown indicating the start of the second wave.

We address the question of the title using a simple SIR model. We first investigate the impact of various confinement strategies. A universal feature of all our simulations is that relaxing the lockdown constraints leads to a rekindling of the epidemic. We thus seek the conditions for the second epidemic peak to be lower than the first one. From our results, the most promising strategy is that of a stepwise exit. And in fact its implementation can be quite feasible, with the major part of the population (minus the fragile groups) exiting simultaneously but obeying rigorous distancing constraints. Focusing on the COVID-19 pandemic we analyse the patterns of the current epidemic evolution in various countries. Two main effects are considered: seasonality and recruitment. The former corresponds to the variation of the infection rate with the season, corresponding essentially to a decrease during the local summer months. The latter is introduced as a way to palliate for the absence of a spatial component in the SIR model. We show that with our model it is possible to reproduce the observed patterns in several countries thanks to simple recruitment assumptions. Finally, in order to show the power of the recruitment approach, we simulate the case of the 1918 influenza epidemic reproducing successfully the, by now famous, three epidemic peaks.

In this study, we use an SEIR epidemic model to estimate the epidemic curve of COVID-19 in Japan. By fitting the model to the early data of newly reported cases from January to　February 2020, we estimate the basic reproduction number Ro for COVID-19 in Japan as 2.6. Moreover, taking into account the effect of people's behavior change during the intervention period, we evaluate the epidemic prevention effect of the first state of emergency for COVID-19 in Japan, which was declared on 7 April 2020 and lifted on 25 May 2020. As a result, we conjecture that the 80% reduction of the contact rate, which was a public slogan during that period, could be successfully achieved. In addition, we discuss the effect of massive testing by using an epidemic model with quarantined classes.