RESUMO
The main objective of this paper is to propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a setup under general latency and infectious period distributions. To some extent, queuing systems with infinitely many servers and a Markov chain with time-varying transition rate comprise the very technical underpinning of the paper. Although more general, the Markov chain is as tractable as previous models for exponentially distributed latency and infection periods. It is also significantly more straightforward and tractable than semi-Markov models with a similar level of generality. Based on stochastic stability, we derive a sufficient condition for a shrinking epidemic regarding the queuing system's occupation rate that drives the dynamics. Relying on this condition, we propose a class of ad-hoc stabilising mitigation strategies that seek to keep a balanced occupation rate after a prescribed mitigation-free period. We validate the approach in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil, and assess the effect of different stabilising strategies in the latter setting. Results suggest that the proposed approach can curb the epidemic with various occupation rate levels if the mitigation is timely.
Assuntos
COVID-19 , Epidemias , Humanos , Processos Estocásticos , COVID-19/epidemiologia , COVID-19/prevenção & controle , Epidemias/prevenção & controle , Cadeias de Markov , Brasil , Modelos BiológicosRESUMO
In this work we study the problem of modeling identification of a population employing a discrete dynamic model based on the Richards growth model. The population is subjected to interventions due to consumption, such as hunting or farming animals. The model identification allows us to estimate the probability or the average time for a population number to reach a certain level. The parameter inference for these models are obtained with the use of the likelihood profile technique as developed in this paper. The identification method here developed can be applied to evaluate the productivity of animal husbandry or to evaluate the risk of extinction of autochthon populations. It is applied to data of the Brazilian beef cattle herd population, and the the population number to reach a certain goal level is investigated.