A time-varying SIRD model for dynamic vaccination strategies against COVID-19

Abstract Introduction The COVID-19 pandemic has demonstrated how the optimal allocation of the limited doses of vaccine available represents one of the main useful measures to mitigate the transmission of the infection and reduce the mortality associated with it, especially at an early stage of the pandemic. The use of a compartmental model allows us to understand which population groups to vaccinate and to what extent to act depending on the type of health or social objective to be achieved. Methods A time-varying susceptible-infected-recovered-deceased (SIRD) compartmental model, stratified into ten age groups, was developed on Italian data. Simulations were performed every 15 days from December 2020 to April 2021. An optimal vaccination strategy was achieved by minimizing deaths or infected, considering the total vaccine doses available. Results We showed how the effects of a vaccination campaign can be planned in a way that maximizes lives saved and/or minimizes infections. Regarding the minimization of deaths, the model prioritizes the elderly (>80 years) and then those between 60 and 80 years, in all simulations. Regarding the cost function of new infections, the first simulation assigns all available doses to those over 90 years of age. In the later simulations, the doses are assigned mainly to the 20-29-year-old and the 89+ year old. Conclusions Optimal allocation of available vaccine doses is useful in mitigating transmission of infection and reducing mortality. Application of the mathematical model can be useful at the beginning of an epidemic caused by a new pathogen, when data are scarce, and it is therefore necessary to introduce a standardized approach. This kind of simulation is useful to understand whether the implemented vaccination strategy needs to be recalibrated, too. Key messages • Time-varying compartmentalised models can be used both to continuously inform decision-makers about changes in epidemic traits and to simulate the effects of targeted pandemic containment strategies. • The application of compartmental models can be very useful at the onset of an epidemic to more successfully contain it and structure the health, political, and economic plan.


Introduction:
The COVID-19 pandemic has demonstrated how the optimal allocation of the limited doses of vaccine available represents one of the main useful measures to mitigate the transmission of the infection and reduce the mortality associated with it, especially at an early stage of the pandemic. The use of a compartmental model allows us to understand which population groups to vaccinate and to what extent to act depending on the type of health or social objective to be achieved.

Methods:
A time-varying susceptible-infected-recovered-deceased (SIRD) compartmental model, stratified into ten age groups, was developed on Italian data. Simulations were performed every 15 days from December 2020 to April 2021. An optimal vaccination strategy was achieved by minimizing deaths or infected, considering the total vaccine doses available.

Results:
We showed how the effects of a vaccination campaign can be planned in a way that maximizes lives saved and/or minimizes infections. Regarding the minimization of deaths, the model prioritizes the elderly (>80 years) and then those between 60 and 80 years, in all simulations. Regarding the cost function of new infections, the first simulation assigns all available doses to those over 90 years of age. In the later simulations, the doses are assigned mainly to the 20-29-year-old and the 89+ year old.

Conclusions:
Optimal allocation of available vaccine doses is useful in mitigating transmission of infection and reducing mortality. Application of the mathematical model can be useful at the beginning of an epidemic caused by a new pathogen, when data are scarce, and it is therefore necessary to introduce a standardized approach. This kind of simulation is useful to understand whether the implemented vaccination strategy needs to be recalibrated, too. Key messages: Time-varying compartmentalised models can be used both to continuously inform decision-makers about changes in epidemic traits and to simulate the effects of targeted pandemic containment strategies. The application of compartmental models can be very useful at the onset of an epidemic to more successfully contain it and structure the health, political, and economic plan. Many elderly people would like to stay in their own homes as long as possible. Therefore, a focus on enabling factors for a healthy aging in place in needed. Italy was the first European country to be hit hard by the pandemic. These had an impact on people's everyday lives, on social participation and freedom of movement for all sections of the population. But especially elderly people were considered a risk group and were urged to leave their homes as little as possible. The project aimed to analyse the situation of elderly people in South Tyrol (Northern Italy), focusing on the characteristics of enabling factors for a healthy ageing in place. The main research question was: What kind of enabling factors ensure a healthy aging in place during the pandemic? Using a mixed-methodsapproach, we conducted 10 semi-structured interviews (experts: social workers, health professionals, responsible persons from senior associations, ...) analysed by qualitative content analysis and a quantitative questionnaire (536 respondents, aged 60 to 101 still living in their own home) from 2020 to 2021. The questionnaire was distributed in digital and analogue form to reach a wider study group and to facilitate access to the research group despite the infection control measures or technical challenges. The results show that there were numerous changes in the everyday life of elderly people during the pandemic, which were described as particularly important for a healthy ageing in place. Based on the answers to the pandemic-related restrictions, 6 categories could be identified: Loneliness versus desire for social contact, mobility, emotions, needs, opportunities, restrictions. To be able to guarantee healthy ageing in place, we need to examine and promote these enabling factors in the long term.

Key messages:
A focus on enabling factors for a healthy aging in place in needed. There were numerous changes in the everyday life of elderly people during the pandemic, which were described as particularly important for a healthy ageing in place.