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.

M. J. Lazo, A. De Cezaro

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.

Keywords


COVID-19; SEIR model; epidemic diseases

Full Text:

PDF

References


S. Ansumali and M. Prakash. A very flat peak: Why standard SEIR models miss the plateau of covid-19 infections and how it can be corrected.medRxiv,2020.

D. Bernoulli. Essai d’une nouvelle analyse de la mortalité causée par la petitevérole, et des avantages de l’inoculation pour la prévenir.Histoire de l’Acad.,Roy. Sci.(Paris) avec Mem, pages 1–45, 1760.

C. Castilho, J. A. M. Godim, M. Marchesin, and M. Sabeti. Assessing the efficiency of different control strategies for coronavirus (covid-19) epidemic. Electronic Journal of Differential Equations, 2020(64):1–17, 2020.

M. Fagundes.Who says brazil’s covid-19 curve has plateaued.https: // www. bloomberg. com/ news/ articles/ 2020-07-17/who-says-brazil-s-covid-19-curve-has-plateaued, 2020.

N. Ferguson and et al. Report 9: Impact of non-pharmaceutical interventions(npis) to reduce covid-19 mortality and healthcare demand.Imperial CollegeCOVID-19 Response Team, pages 1–20, 2020.

G. Giordano, F. Blanchini, R. Bruno, and et al. Modelling the covid-19 epi-demic and implementation of population-wide interventions in italy. Nat Med,26:855–860, 2020.

J. Govaert. Coronavirus: Uk changes course amid death toll fears. https:// www. bbc. com/ news/ health-51915302, 2020.

J. N. Hays.Epidemics and pandemics: their impacts on human history. Abc-clio, 2005.

S. He, Y. Peng, and K. Sun. SEIR modeling of the covid-19 and its dynamics.Nonlinear Dyn, pages doi.org/10.1007/s11071–020–05743–y, 2020.

H. W. Hethcote. Three basic epidemiological models. In Applied mathematical ecology, pages 119–144. Springer, 1989.

H. W. Hethcote. The mathematics of infectious diseases. SIAM review, 42(4):599–653, 2000.

M. Keeling and P. Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, 2007.

W. Kermack and A. Mckendrick. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, Containing papers of a Mathematical and Physical Character, 115(772):700–721, 1927.

B. Lima and M. Cardim. Covid-19 no brasil: mortes se estabilizam em platô nas alturas.https: // www. correiobraziliense.com. br/ app/ noticia/ brasil/ 2020/ 07/ 12/ interna-brasil,871435/covid-19-no-brasil-mortes-se-estabilizam-em-plato-nas-alturas.shtml, 2020.

A. Nande, B. Adlam, J. Sheen, M. Z. Levy, and A. L. Hill. Dynamics of covid-19under social distancing measures are driven by transmission network structure.medRxiv, 2020.

M. of Health of Brazil. Painel coronavírus.https: // covid. saude. gov. br/,2020.

C. Oliveira. Reopening in SP is sending "population to a slaughterhouse", warns COVID specialist.Brasil de Fato, 2020/07/12, 2020.

W. H. Organization. Who coronavirus disease (covid-19) dashboard https://covid19.who.int 2020/7/29, 2020.

A. Park. Here’s how scientists and public-health experts recommend the u.s. gets back to ’normal’.TIME, 2020/04/30, 2020.

K. e. Prem. The effect of control strategies to reduce social mixing on outcomes of the covid-19 epidemic in Wuhan, China: a modeling study. Lancet PublicHealth, 5:e261–70, 2020.

J. Sotomayor.Lições de Equações Diferenciais Ordinárias, volume 11. Institutode Matemática Pura e Aplicada, CNPq, 1979.

A. Teimouri. An SEIR model with contact tracing and age-structured social mixing for COVID-19 outbreak.medRxiv, 2020.

B. M. e. a. Wu J.T., Leung K. Estimating clinical severity of covid-19 from the transmission dynamics in Wuhan, China. Nat. Med., pageshttps://doi.org/10.1038/s41591–020–0822–7, 2020.




DOI: https://doi.org/10.5540/tcam.2021.022.01.00109

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia