Basil Grammaticos


Nakamura G., Grammaticos B., Badoual M.
We analyse the patterns of the current epidemic evolution in various countries with the help of a simple SIR model. We consider two main effects: climate induced seasonality and recruitment. The latter is introduced as a way to palliate for the absence of a spatial component in the SIR model. In our approach we mimic the spatial evolution of the epidemic through a gradual introduction of susceptible individuals.
We apply our model to the case of France and Australia and explain the appearance of two temporally well-separated epidemic waves. We examine also Brazil and the USA, which present patterns very different from those of the European countries. We show that with our model it is possible to reproduce the observed patterns in these two 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.
Keywords: epidemic, modelling, SIR model, seasonality, recruitment
Citation: Nakamura G., Grammaticos B., Badoual M.,  Recruitment Effects on the Evolution of Epidemics in a Simple SIR Model, Regular and Chaotic Dynamics, 2021, vol. 26, no. 3, pp. 305-319
Nakamura G., Grammaticos B., Badoual M.
Confinement Strategies in a Simple SIR Model
2020, vol. 25, no. 6, pp.  509-521
We propose a simple deterministic, differential equation-based, SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two populations of susceptible persons, one which obeys confinement and for which the infection rate does not exceed 1, and a population which, being non confined for various imperatives, can be substantially more infective. The model, initially formulated as a differential system, is discretised following a specific procedure, the discrete system serving as an integrator for the differential one. Our model is calibrated so as to correspond to what is observed in the COVID-19 epidemic, for the period from February 19 to April 16.
Several conclusions can be reached, despite the very simple structure of our model. First, it is not possible to pinpoint the genesis of the epidemic by just analysing data from when the epidemic is in full swing. It may well turn out that the epidemic has reached a sizeable part of the world months before it became noticeable. Concerning the confinement scenarios, a universal feature of all our simulations is that relaxing the lockdown constraints leads to a rekindling of the epidemic. Thus, we sought the conditions for the second epidemic peak to be lower than the first one. This is possible in all the scenarios considered (abrupt or gradualexit, the latter having linear and stepwise profiles), but typically a gradual exit can start earlier than an abrupt one. However, by the time the gradual exit is complete, the overall confinement times are not too different. From our results, the most promising strategy is that of a stepwise exit. Its implementation could be quite feasible, with the major part of the population (perhaps, minus the fragile groups) exiting simultaneously, but obeying rigorous distancing constraints.
Keywords: epidemics, modelling, SIR model, lockdown
Citation: Nakamura G., Grammaticos B., Badoual M.,  Confinement Strategies in a Simple SIR Model, Regular and Chaotic Dynamics, 2020, vol. 25, no. 6, pp. 509-521

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