Results from a fuzzy model show that intervention measures impede the spread of COVID-19 even with the vaccine

Glaucia Maria Bressan, Universidade Tecnológica Federal do Paraná, Departamento de Matemática, Cornélio Procópio, Paraná, Brasil.

Elenice Weber Stiegelmeier, Universidade Tecnológica Federal do Paraná, Departamento de Matemática, Cornélio Procópio, Paraná, Brasil.

The spread of COVID-19 pandemic has motivated the development of studies and several research activities have been conducted for better understanding the origin, treatments and preventions of this virus.

This paper intitled Fuzzy Modelling on the Evolution of COVID-19 Epidemic under the Effects of Intervention Measures, written by Dr. Glaucia Maria Bressan and Dr. Elenice Weber Stiegelmeier, proposes to analyze how the intervention measures such as lockdown, partial lockdown and no-lockdown help to impede the spread of the severe outbreak of COVID-19 in Brazil. A p-fuzzy model, considering as input variables, the infected population and the intervention measures and as output variable the level of infestation, is proposed.

World Health Organization (WHO)¹ recommends that intervention measures, such as personal protective measures (hand hygiene, respiratory etiquette, mask wearing), environmental measures and physical distancing measures, are still necessary, even with the vaccine. Relaxing social distancing restrictions to the pre-pandemic level would lead to a new COVID-19 outbreak.

Imagem: Pixabay.

In this context, a mathematical model using a discrete p-fuzzy system, is formulated, considering intervention measures for COVID-19 control. The input variables of the fuzzy system are the infected population and the intervention measures, which consists of social distancing such as lockdown, partial lockdown and no-lockdown. The output variable is the level of infestation. Numerical analysis is performed considering as simulation scenario. The proposed fuzzy model shows that intervention measures play a crucial role in COVID-19 eradication programs, while the population is being vaccinated in stages.

The results showed that to consider medium-high lockdown helped to slow down the transmission rates of COVID-19 in the population, however the total lockdown is more effective, while the population has been vaccinated. In addition, the second wave of the pandemic, or the second cycle of the virus, has been more aggressive than the first one and the results presented in this paper demonstrate this fact, as illustrated in Figure 1.

Image: BRESSAN, G.M. and STIEGELMEIER, E.W.

Figure 1. P-fuzzy model solution with (a) no-lockdown active; (b) medium-low lockdown is active; (c) medium-high lockdown is active and (d) total-lockdown is active.

In addition, mathematical models indicate that the only way to stop the spread of COVID-19 is the social isolation measures²³⁴⁵⁶. In this sense, these results converge with the results presented by the fuzzy model proposed in this paper. Physical distancing measures together with upcoming vaccines can contain the spread and the resurgences of the disease. The distancing make sure people are protected against COVID-19 till the pandemic ceases to pose a threat to personal or public health⁵.

Therefore, the proposed fuzzy model contributes to minimize the risk of infection when social distancing was adopted. Results can assist government decision making in order to minimize the economic impacts caused by the pandemic and these prevention measures lead to a sudden decline in transmission rate of COVID-19 and turn out to be an effective strategy in containing the virus and saving lives.

References

[1] WHO World Health Organization. Considerations for implementing and adjusting public health and social measures in the context of covid-19, Interim guidance. 2020 [viewed 4 January 2023]. Available from: www.who.int/news-room/q-a-detail/q-acoronaviruses

[2] GRZYBOWSKI, J., SILVA, R. and RAFIKOV, M. Expanded seircq model applied to covid-19 epidemic control strategy design and medical infrastructure planning. Math. Probl. Eng. [online]. 2020, 8198563 [viewed 4 January 2023]. https://doi.org/10.1155/2020/8198563. Available from: https://www.hindawi.com/journals/mpe/2020/8198563/

[3] SHEN, S.M., et al. Projected covid-19 epidemic in the United States in the context of the effectiveness of a potential vaccine and implications for social distancing and face mask use. Vaccine [online]. 2021, vol. 39, no. 16, pp. 2295-2302 [viewed 4 January 2023]. https://doi.org/10.1016/j.vaccine.2021.02.056. Available from: https://www.sciencedirect.com/science/article/pii/S0264410X2100236X?via%3Dihub

[4] HUANG, B., et al. Integrated vaccination and physical distancing interventions to prevent future Covid-19 waves in chinese cities. Nat. Hum. Behav. [online]. 2021, vol. 5, no. 6, pp. 695-705 [viewed 4 January 2023]. https://doi.org/10.1038/s41562-021-01063-2. Available from: https://www.nature.com/articles/s41562-021-01063-2

[5] SU, Z., et al. Vaccines are not yet a silver bullet: The imperative of continued communication about the importance of Covid-19 safety measures. Brain Behav. Immun. [online]. 2021, vol. 12, 100204 [viewed 4 January 2023]. https://doi.org/10.1016/j.bbih.2021.100204. Available from: https://www.sciencedirect.com/science/article/pii/S2666354621000077?via%3Dihub

[6] WANG, N., et al. An evaluation of mathematical models for the outbreak of Covid-19. Precis. Clin. Med. [online]. 2020, vol. 3, no. 2, pp. 85-93 [viewed 4 January 2023]. https://doi.org/10.1093/pcmedi/pbaa016. Available from: https://academic.oup.com/pcm/article/3/2/85/5841934

To read the article, access

BRESSAN, G.M. and STIEGELMEIER, E.W. Fuzzy Modelling on the Evolution of COVID-19 Epidemic under the Effects of Intervention Measures. Braz. arch. biol. technol. [online]. 2023, vol. 66, e23220425 [viewed 4 January 2023]. https://doi.org/10.1590/1678-4324-2023220425. Available from: https://www.scielo.br/j/babt/a/bNSbQvbH8pCcwpsbFcxsXzS/

External links

Brazilian Archives of Biology and Technology – BABT: https://www.scielo.br/j/babt/

To read the BABT latest edition, access: https://www.scielo.br/j/babt/i/2023.v66/

Universidade Tecnológica Federal Do Paraná – Instagram: https://www.instagram.com/utfpr_cp/

Glaucia Maria Bressan: Orcid | Lattes | Scholar Google

Elenice Weber Stiegelmeier: Orcid | Lattes