Determination of an optimal control strategy for vaccine administration in COVID-19 pandemic treatment

Integrated vaccination and non-pharmaceutical interventions based strategies in Ontario, Canada, as a case study: a mathematical modelling study

Recently, two coronavirus disease 2019 (COVID-19) vaccine products have been authorized in Canada. It is of crucial importance to model an integrated/combined package of non-pharmaceutical (physical/social distancing) and pharmaceutical (immunization) public health control measures. A modified epidemiological, compartmental SIR model was used and fit to the cumulative COVID-19 case data for the province of Ontario, Canada, from 8 September 2020 to 8 December 2020. Different vaccine roll-out strategies were simulated until 75% of the population was vaccinated, including a no-vaccination scenario. We compete these vaccination strategies with relaxation of non-pharmaceutical interventions. Non-pharmaceutical interventions were supposed to remain enforced and began to be relaxed on 31 January, 31 March or 1 May 2021. Based on projections from the data and long-term extrapolation of scenarios, relaxing the public health measures implemented by re-opening too early would cause any benefits of vaccination to be lost by increasing case numbers, increasing the effective reproduction number above 1 and thus increasing the risk of localized outbreaks. If relaxation is, instead, delayed and 75% of the Ontarian population gets vaccinated by the end of the year, re-opening can occur with very little risk. Relaxing non-pharmaceutical interventions by re-opening and vaccine deployment is a careful balancing act. Our combination of model projections from data and simulation of different strategies and scenarios, can equip local public health decision- and policy-makers with projections concerning the COVID-19 epidemiological trend, helping them in the decision-making process.

Integrated vaccination and non-pharmaceutical interventions based strategies in Ontario, Canada, as a case study: a mathematical modelling study

Recently, two coronavirus disease 2019 (COVID-19) vaccine products have been authorized in Canada. It is of crucial importance to model an integrated/combined package of non-pharmaceutical (physical/social distancing) and pharmaceutical (immunization) public health control measures. A modified epidemiological, compartmental SIR model was used and fit to the cumulative COVID-19 case data for the province of Ontario, Canada, from 8 September 2020 to 8 December 2020. Different vaccine roll-out strategies were simulated until 75% of the population was vaccinated, including a no-vaccination scenario. We compete these vaccination strategies with relaxation of non-pharmaceutical interventions. Non-pharmaceutical interventions were supposed to remain enforced and began to be relaxed on 31 January, 31 March or 1 May 2021. Based on projections from the data and long-term extrapolation of scenarios, relaxing the public health measures implemented by re-opening too early would cause any benefits of vaccination to be lost by increasing case numbers, increasing the effective reproduction number above 1 and thus increasing the risk of localized outbreaks. If relaxation is, instead, delayed and 75% of the Ontarian population gets vaccinated by the end of the year, re-opening can occur with very little risk. Relaxing non-pharmaceutical interventions by re-opening and vaccine deployment is a careful balancing act. Our combination of model projections from data and simulation of different strategies and scenarios, can equip local public health decision- and policy-makers with projections concerning the COVID-19 epidemiological trend, helping them in the decision-making process.

Socio-demographic and health factors drive the epidemic progression and should guide vaccination strategies for best COVID-19 containment

We propose and study an epidemiological model on a social network that takes into account heterogeneity of the population and different vaccination strategies. In particular, we study how the COVID-19 epidemics evolves and how it is contained by different vaccination scenarios by taking into account data showing that older people, as well as individuals with comorbidities and poor metabolic health, and people coming from economically depressed areas with lower quality of life in general, are more likely to develop severe COVID-19 symptoms, and quicker loss of immunity and are therefore more prone to reinfection. Our results reveal that the structure and the spatial arrangement of subpopulations are important epidemiological determinants. In a healthier society the disease spreads more rapidly but the consequences are less disastrous as in a society with more prevalent chronic comorbidities. If individuals with poor health are segregated within one community, the epidemic outcome is less favorable. Moreover, we show that, contrary to currently widely adopted vaccination policies, prioritizing elderly and other higher-risk groups is beneficial only if the supply of vaccine is high. If, however, the vaccination availability is limited, and if the demographic distribution across the social network is homogeneous, better epidemic outcomes are achieved if healthy people are vaccinated first. Only when higher-risk groups are segregated, like in elderly homes, their prioritization will lead to lower COVID-19 related deaths. Accordingly, young and healthy individuals should view vaccine uptake as not only protecting them, but perhaps even more so protecting the more vulnerable socio-demographic groups.

Potential impact of introducing vaccines against COVID-19 under supply and uptake constraints in France: A modelling study

BACKGROUND

The accelerated vaccine development in response to the COVID-19 pandemic should lead to a vaccine being available early 2021, albeit in limited supply and possibly without full vaccine acceptance. We assessed the short-term impact of a COVID-19 immunization program with varying constraints on population health and non-pharmaceutical interventions (NPIs) needs.

METHODS

A SARS-CoV-2 transmission model was calibrated to French epidemiological data. We defined several vaccine implementation scenarios starting in January 2021 based on timing of discontinuation of NPIs, supply and uptake constraints, and their relaxation. We assessed the number of COVID-19 hospitalizations averted, the need for and number of days with NPIs in place over the 2021-2022 period.

RESULTS

An immunisation program under constraints could reduce the burden of COVID-19 hospitalizations by 9-40% if the vaccine prevents against infections. Relaxation of constraints not only reduces further COVID-19 hospitalizations (30-39% incremental reduction), it also allows for NPIs to be discontinued post-2021 (0 days with NPIs in 2022 versus 11 to 125 days for vaccination programs under constraints and 327 in the absence of vaccination).

CONCLUSION

For 2021, COVID-19 control is expected to rely on a combination of NPIs and the outcome of early immunisation programs. The ability to overcome supply and uptake constraints will help prevent the need for further NPIs post-2021. As the programs expand, efficiency assessments will be needed to ensure optimisation of control policies post-emergency use.

Stability analysis of SEIR model related to efficiency of vaccines for COVID-19 situation

This work is aimed to formulate and analyze a mathematical modeling, SEIR model, for COVID-19 with the main parameters of vaccination rate, effectiveness of prophylactic and therapeutic vaccines. Global and local stability of the model are investigated and also numerical simulation. Local stability of equilibrium points are classified. A Lyapunov function is constructed to analyze global stability of the disease-free equilibrium. The simulation part is based on two situations, the US and India. In the US circumstance, the result shows that with the rate of vaccination 0.1% per day of the US population and at least 20% effectiveness of both prophylactic and therapeutic vaccines, the reproductive numbers R0 are reduced from 2.99 (no vaccine) to less than 1. The same result happens in India case where the maximum reproductive number R0 in this case is 3.38. To achieve the same infected level of both countries, the simulation shows that with the same vaccine's efficiency the US needs a higher vaccination rate per day. Without vaccines for this pandemic, the model shows that a few percentages of the populations will suffering from the disease in the long term.

A Two-Phase Stochastic Dynamic Model for COVID-19 Mid-Term Policy Recommendations in Greece: A Pathway towards Mass Vaccination

From 7 November 2020, Greece adopted a second nationwide lockdown policy to mitigate the transmission of SARS-CoV-2 (the first took place from 23 March to 4 May 2020), just as the second wave of COVID-19 was advancing, as did other European countries. To secure the full benefits of mass vaccination, which started in early January 2021, it is of utmost importance to complement it with mid-term non-pharmaceutical interventions (NPIs). The objective was to minimize human losses and to limit social and economic costs. In this paper a two-phase stochastic dynamic network compartmental model (a pre-vaccination SEIR until 15 February 2021 and a post-vaccination SVEIR from 15 February 2021 to 30 June 2021) is developed. Three scenarios are assessed for the first phase: (a) A baseline scenario, which lifts the national lockdown and all NPIs in January 2021; (b) a "semi-lockdown" scenario with school opening, partial retail sector operation, universal mask wearing, and social distancing/teleworking in January 2021; and (c) a "rolling lockdown" scenario combining a partial lifting of measures in January 2021 followed by a third nationwide lockdown in February 2021. In the second phase three scenarios with different vaccination rates are assessed. Publicly available data along with some first results of the SHARE COVID-19 survey conducted in Greece are used as input. The results regarding the first phase indicate that the "semi-lockdown" scenario clearly outperforms the third lockdown scenario (5.7% less expected fatalities); the second phase is extremely sensitive on the availability of sufficient vaccine supplies and high vaccination rates.

Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal

The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to "normal life" and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.

Mathematical modelling of the second wave of COVID-19 infections using deterministic and stochastic SIDR models

Recently, various countries from across the globe have been facing the second wave of COVID-19 infections. In order to understand the dynamics of the spread of the disease, much effort has been made in terms of mathematical modeling. In this scenario, compartmental models are widely used to simulate epidemics under various conditions. In general, there are uncertainties associated with the reported data, which must be considered when estimating the parameters of the model. In this work, we propose an effective methodology for estimating parameters of compartmental models in multiple wave scenarios by means of a dynamic data segmentation approach. This robust technique allows the description of the dynamics of the disease without arbitrary choices for the end of the first wave and the start of the second. Furthermore, we adopt a time-dependent function to describe the probability of transmission by contact for each wave. We also assess the uncertainties of the parameters and their influence on the simulations using a stochastic strategy. In order to obtain realistic results in terms of the basic reproduction number, a constraint is incorporated into the problem. We adopt data from Germany and Italy, two of the first countries to experience the second wave of infections. Using the proposed methodology, the end of the first wave (and also the start of the second wave) occurred on 166 and 187 days from the beginning of the epidemic, for Germany and Italy, respectively. The estimated effective reproduction number for the first wave is close to that obtained by other approaches, for both countries. The results demonstrate that the proposed methodology is able to find good estimates for all parameters. In relation to uncertainties, we show that slight variations in the design variables can give rise to significant changes in the value of the effective reproduction number. The results provide information on the characteristics of the epidemic for each country, as well as elements for decision-making in the economic and governmental spheres.

Identification of an Epidemiological Model to Simulate the COVID-19 Epidemic Using Robust Multiobjective Optimization and Stochastic Fractal Search

Traditionally, the identification of parameters in the formulation and solution of inverse problems considers that models, variables, and mathematical parameters are free of uncertainties. This aspect simplifies the estimation process, but does not consider the influence of relatively small changes in the design variables in terms of the objective function. In this work, the SIDR (Susceptible, Infected, Dead, and Recovered) model is used to simulate the dynamic behavior of the novel coronavirus disease (COVID-19), and its parameters are estimated by formulating a robust inverse problem, that is, considering the sensitivity of design variables. For this purpose, a robust multiobjective optimization problem is formulated, considering the minimization of uncertainties associated with the estimation process and the maximization of the robustness parameter. To solve this problem, the Multiobjective Stochastic Fractal Search algorithm is associated with the Effective Mean concept for the evaluation of robustness. The results obtained considering real data of the epidemic in China demonstrate that the evaluation of the sensitivity of the design variables can provide more reliable results.