# Applied Mathematics and Numerical Analysis Seminar

## Planned sessions

### Modelling the transmission dynamics of SARS-CoV-2 in Portugal

In March 11th of 2020, the World Health Organization declared the COVID-19 global public health emergency a pandemic [1]. Since the appearance of the first cases in Wuhan, China, several countries have employed the use of mathematical and statistical techniques to ascertain the course of the disease spread. The most common mathematical tool available to model such phenomena are systems of differential equations. The most notable are the SIR and SEIR model first developed by Kermack and McKendrick (1927). These models have been used to study an array of different epidemic questions. At the start of the pandemic, these models were employed to nowcast and forecast the national spread of SARS-CoV-2 in China. In [2] the authors create scenarios of transmissibility reduction and mobility reduction associated with the measures employed by the Chinese government. Similar models were also used to estimate the proportion of susceptible individuals in a population, i.e. how much is the case ascertainment in a given country [3]. This topic is very important since it has been shown that a high percentage of infected individuals do not develop symptoms [4] but are still able to infect others [5]. The main purpose of these modelling techniques has been to evaluate the impact of contagion mitigation measures, such as the closure of schools and lockdowns [6].

In Portugal, the team at the department of epidemiology Instituto Nacional de Saúde Doutor Ricardo Jorge, has been, since the start of the epidemic developing reports with an array of different statistical and mathematical procedures [7], in order to present a clear picture of the evolution of the epidemic, with the objective of supporting public health policy making. Part of this work involved building a SEIR-type model with heterogeneous mixing among age groups. This model was key to provide some evidence on the impact of the lockdown in Portugal from March 22th until May 4th. Using data from google mobility reports [8], the model showed that a decrease in transmission was expect after the implementation of the lockdown, which was not yet noticeable due to the delay between infection and case notification.

With the increase, as of late, of the daily incidence of COVID-19 cases and with the opening of schools, public health decision makers need to know what will be the expected impact on the Portuguese health system, and what non-pharmaceutical-interventions (NPI) can be adapted in order to compensate for such increase. Several epidemiologist state that higher and faster contact tracing might be the best and most efficient measure to compensate for such increase. The team is currently developing a new model that takes into account several NPIs, such as contact tracing, case ascertainment, mask usage, shielding of vulnerable (elderly) individuals, and closure/opening of schools, among others. The main objective is to provide possible scenarios for the magnitude of the impact of these measures.

Joint work with:

• Paula Patrício, Centro de Matemática e Aplicações & Departamento de Matemática Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa
• Baltazar Nunes, Instituto Nacional de Saúde Doutor Ricardo Jorge

#### References

1. ECDC: Event Background-COVID-19.
2. Wu, J. T., Leung, K., & Leung, G. M. (2020). Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. The Lancet, 395(10225), 689–697. doi: 10.1016/s0140-6736(20)30260-9
3. Maugeri A, Barchitta M, Battiato S, Agodi A. Estimation of Unreported Novel Coronavirus (SARS-CoV-2) Infections from Reported Deaths: A Susceptible-Exposed-Infectious-Recovered-Dead Model. J Clin Med. 2020;9(5):1350. Published 2020 May 5. doi:10.3390/jcm9051350
4. Instituto Nacional de Saúde Dr. Ricardo Jorge (2020). Relatório de Apresentação dos Resultados Preliminares do Primeiro Inquérito Serológico Nacional COVID-19. Available: (acesso a 25/08/2020)
5. Huang L-S, Li L, Dunn L, He M. Taking. Account of Asymptomatic Infections in Modeling the Transmission Potential of the COVID-19 Outbreak on the Diamond Princess Cruise Ship. medRxiv. 2020:2020.04.22.20074286.
6. Prem, K., Liu, Y., Russell, T., Kucharski, A. J., Eggo, R. M., Davies, N., Jit, M. Klepac, P. (2020). The effect of control strategies that reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China. The Lancet Public Health. doi: 10.1101/2020.03.09.20033050
7. Nunes B, Caetano C, Antunes L, et al. Evolução do número de casos de COVID-19 em Portugal. Relatório de nowcasting. Inst. Nac. Saúde Doutor Ricardo Jorge. 2020;