Why Can We Observe a Plateau Even in an Out of Control Epidemic Outbreak? A SEIR Model With the Interaction of n Distinct Populations for Covid-19 in Brazil.

Abstract

This manuscript proposes a model of $n$ distinct populations interaction structured SEIR to describe the spread of COVID-19 pandemic diseases. The proposed model has the flexibility to include geographically separated communities as well as taking into account aging population groups and their interactions. We show that distinct assumptions on the dynamics of the proposed model lead to a plateau-like curve of the infected population, reflecting collected data from large countries like Brazil. Such observations aim to the following conjecture: " Covid-19 diseased diffusion from the capitals to the Brazil interior, as reflected by the proposed model, is responsible for plateau-like reported cases in the country". We present numerical simulations of some scenarios and comparison with reported data from Brazil that corroborate with the aforementioned conclusions.

Dynamic Systems with Fractional Derivatives Applied to Interagent Populations Problems

“…This extension can describe, for example, the spread of the disease between neighborhoods and neighboring cities. Diffusion produces an increase in the period of the epidemic because, in each neighborhood and city, the peak of infection occurs at a different time [6], as we will see in our model when considering the interaction between two cities. For the results presented in Figure 2 we used N 1 = 211965 (data from the population of Rio Grande obtained through the website https://www.riogrande.rs.gov.br/pagina/284-anos-riogrande-mantem-forte-potencial-economico-e-turistico/ (Rio Grande City Hall)), β 11 = 1, γ 1 = 0.5, κ 1 = 0 (for simplicity, we do not consider death cases) and µ 1 = 0.001.…”

“…Finally, it can be seen that the curve does not describe well the cases reported by the official data, since the real dynamics show an approximately linear growth. According to [6] this linear growth may be an indication of the spread of the disease to neighboring cities and between neighborhoods of the same city. This fact leads to anomalous growth dynamics, which motivates the investigation of models of interacting populations and fractional models.…”

“…Finally, in the context of interacting populations, the work [6] proposes a structured SEIR (susceptible-exposed-infected-recovered) model for the interaction of n different populations to describe the spread of pandemic diseases such as COVID-19. For the authors, the proposed model has the flexibility to include geographically separate communities, as well as taking into account other groups (for example, age groups) and their interactions.…”

Severe acute respiratory syndrome and COVID-19 under the hierarchy of the urban network of municipalities in the state of Acre, western Brazilian Amazon region, 2020-2021: a cross-sectional study

“…Reinforcing our findings, a structured compartmental model (in agreement with data observed in large countries such as Brazil) indicated that maintenance of a high number of COVID-19 cases in Brazil could be supported by the geographical spread of the disease, which would occur from the state capitals to the interior of the country. 28 Nevertheless, there was little connection between the municipalities in the middle of the state (Jordão, Marechal Thaumaturgo, Porto Walter and Santa Rosa do Purus), which is a possible explanation for the lower rates/intensities of SARS in these cities (Figures 3 and 4). This can be explained by the low circulation of people between these municipalities, which would tend to give rise to low circulation of the disease.…”

“…Reinforcing our findings, a structured compartmental model (in agreement with data observed in large countries such as Brazil) indicated that maintenance of a high number of COVID-19 cases in Brazil could be supported by the geographical spread of the disease, which would occur from the state capitals to the interior of the country. 28 …”