Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

Effects of non-pharmaceutical interventions on COVID-19 transmission: rapid review of evidence from Italy, the United States, the United Kingdom, and China

Background

Prior to the development of COVID-19 vaccines, policymakers instituted various non-pharmaceutical interventions (NPIs) to limit transmission. Prior studies have attempted to examine the extent to which these NPIs achieved their goals of containment, suppression, or mitigation of disease transmission. Existing evidence syntheses have found that numerous factors limit comparability across studies, and the evidence on NPI effectiveness during COVID-19 pandemic remains sparse and inconsistent. This study documents the magnitude and variation in NPI effectiveness in reducing COVID-19 transmission (i.e., reduction in effective reproduction rate [Reff] and daily contact rate) in Italy, the United States, the United Kingdom, and China.

Methods

Our rapid review and narrative synthesis of existing research identified 126 studies meeting our screening criteria. We selected four contexts with >5 articles to facilitate a meaningful synthesis. This step yielded an analytic sample of 61 articles that used data from China, Italy, the United Kingdom, and the United States.

Results

We found wide variation and substantial uncertainty around the effectiveness of NPIs at reducing disease transmission. Studies of a single intervention or NPIs that are the least stringent had estimated Reff reductions in the 10-50% range; those that examined so-called "lockdowns" were associated with greater Reff reductions that ranged from 40 to 90%, with many in the 70-80% range. While many studies reported on multiple NPIs, only six of the 61 studies explicitly used the framing of "stringency" or "mild versus strict" or "tiers" of NPIs, concepts that are highly relevant for decisionmakers.

Conclusion

Existing evidence suggests that NPIs reduce COVID-19 transmission by 40 to 90 percent. This paper documents the extent of the variation in NPI effectiveness estimates and highlights challenges presented by a lack of standardization in modeling approaches. Further research on NPI effectiveness at different stringency levels is needed to inform policy responses to future pandemics.

Mathematical modeling of infectious diseases and the impact of vaccination strategies

Mathematical modeling plays a crucial role in understanding and combating infectious diseases, offering predictive insights into disease spread and the impact of vaccination strategies. This paper explored the significance of mathematical modeling in epidemic control efforts, focusing on the interplay between vaccination strategies, disease transmission rates, and population immunity. To facilitate meaningful comparisons of vaccination strategies, we maintained a consistent framework by fixing the vaccination capacity to vary from 10 to 100% of the total population. As an example, at a 50% vaccination capacity, the pulse strategy averted approximately 45.61% of deaths, while continuous and hybrid strategies averted around 45.18 and 45.69%, respectively. Sensitivity analysis further indicated that continuous vaccination has a more direct impact on reducing the basic reproduction number $ R_0 $ compared to pulse vaccination. By analyzing key parameters such as $ R_0 $, pulse vaccination coefficients, and continuous vaccination parameters, the study underscores the value of mathematical modeling in shaping public health policies and guiding decision-making during disease outbreaks.

Non-pharmaceutical interventions to reduce COVID-19 transmission in the UK: a rapid mapping review and interactive evidence gap map

BACKGROUND

Non-pharmaceutical interventions (NPIs) were crucial in the response to the COVID-19 pandemic, although uncertainties about their effectiveness remain. This work aimed to better understand the evidence generated during the pandemic on the effectiveness of NPIs implemented in the UK.

METHODS

We conducted a rapid mapping review (search date: 1 March 2023) to identify primary studies reporting on the effectiveness of NPIs to reduce COVID-19 transmission. Included studies were displayed in an interactive evidence gap map.

RESULTS

After removal of duplicates, 11 752 records were screened. Of these, 151 were included, including 100 modelling studies but only 2 randomized controlled trials and 10 longitudinal observational studies.Most studies reported on NPIs to identify and isolate those who are or may become infectious, and on NPIs to reduce the number of contacts. There was an evidence gap for hand and respiratory hygiene, ventilation and cleaning.

CONCLUSIONS

Our findings show that despite the large number of studies published, there is still a lack of robust evaluations of the NPIs implemented in the UK. There is a need to build evaluation into the design and implementation of public health interventions and policies from the start of any future pandemic or other public health emergency.

An SIR model with viral load-dependent transmission

The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals' viral load in the disease transmission by proposing a new susceptible-infectious-recovered epidemic model for the densities and mean viral loads of each compartment. To this aim, we formally derive the compartmental model from an appropriate microscopic one. Firstly, we consider a multi-agent system in which individuals are identified by the epidemiological compartment to which they belong and by their viral load. Microscopic rules describe both the switch of compartment and the evolution of the viral load. In particular, in the binary interactions between susceptible and infectious individuals, the probability for the susceptible individual to get infected depends on the viral load of the infectious individual. Then, we implement the prescribed microscopic dynamics in appropriate kinetic equations, from which the macroscopic equations for the densities and viral load momentum of the compartments are eventually derived. In the macroscopic model, the rate of disease transmission turns out to be a function of the mean viral load of the infectious population. We analytically and numerically investigate the case that the transmission rate linearly depends on the viral load, which is compared to the classical case of constant transmission rate. A qualitative analysis is performed based on stability and bifurcation theory. Finally, numerical investigations concerning the model reproduction number and the epidemic dynamics are presented.

The SAITS epidemic spreading model and its combinational optimal suppression control

In this paper, an SAITS epidemic model based on a single layer static network is proposed and investigated. This model considers a combinational suppression control strategy to suppress the spread of epidemics, which includes transferring more individuals to compartments with low infection rate and with high recovery rate. The basic reproduction number of this model is calculated and the disease-free and endemic equilibrium points are discussed. An optimal control problem is formulated to minimize the number of infections with limited resources. The suppression control strategy is investigated and a general expression for the optimal solution is given based on the Pontryagin's principle of extreme value. The validity of the theoretical results is verified by numerical simulations and Monte Carlo simulations.

Infectious Disease Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect

We propose a framework for the description of the effects of vaccinations on the spreading of an epidemic disease. Different vaccines can be dosed, each providing different immunization times and immunization levels. Differences due to individuals' ages are accounted for through the introduction of either a continuous age structure or a discrete set of age classes. Extensions to gender differences or to distinguish fragile individuals can also be considered. Within this setting, vaccination strategies can be simulated, tested and compared, as is explicitly described through numerical integrations.