The optimal lockdown intensity for COVID-19

The complex interplay between risk tolerance and the spread of infectious diseases

Risk-driven behaviour provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the population with regard to risk tolerance. The interplay between behaviour and epidemiology leads to a rich set of possible epidemic dynamics. Depending on the behavioural composition of the population, we find that increasing heterogeneity in risk tolerance can either increase or decrease the epidemic size. We find that multiple waves of infection can arise due to the interplay between transmission and behaviour, even without the replenishment of susceptibles. We find that increasing protective mechanisms such as the effectiveness of interventions, the fraction of risk-averse people in the population and the duration of intervention usage reduce the epidemic overshoot. When the protection is pushed past a critical threshold, the epidemic dynamics enter an underdamped regime where the epidemic size exactly equals the herd immunity threshold and overshoot is eliminated. Finally, we can find regimes where epidemic size does not monotonically decrease with a population that becomes increasingly risk-averse.

A conceptual health state diagram for modelling the transmission of a (re)emerging infectious respiratory disease in a human population

Mathematical modelling of (re)emerging infectious respiratory diseases among humans poses multiple challenges for modellers, which can arise as a result of limited data and surveillance, uncertainty in the natural history of the disease, as well as public health and individual responses to outbreaks. Here, we propose a COVID-19-inspired health state diagram (HSD) to serve as a foundational framework for conceptualising the modelling process for (re)emerging respiratory diseases, and public health responses, in the early stages of their emergence. The HSD aims to serve as a starting point for reflection on the structure and parameterisation of a transmission model to assess the impact of the (re)emerging disease and the capacity of public health interventions to control transmission. We also explore the adaptability of the HSD to different (re)emerging diseases using the characteristics of three respiratory diseases of historical public health importance. We outline key questions to contemplate when applying and adapting this HSD to (re)emerging infectious diseases and provide reflections on adapting the framework for public health-related interventions.

Critical appraisal of how COVID-19 infection and imposed lockdowns have impacted gastroesophageal reflux: A review

Previous literature has demonstrated that COronaVIrus Disease of 2019 (COVID-19) impacts an individual gastrointestinal tract (GIT), causing symptoms like nausea, diarrhea, and loss of appetite. Severe acute respiratory syndrome coronavirus RNA has been discovered in the stool of infected individuals in earlier research. It was discovered that severe acute respiratory syndrome coronavirus was significantly expressed in the GIT, indicating that the virus can also infect the digestive system. Angiotensin-converting enzyme 2 functions as the viral receptor. The chronic illness known as gastroesophageal reflux disease (GERD) is typified by frequent reflux of stomach acid into the esophagus. By triggering the sensitized esophageal-bronchial neuronal circuit or aspirating into the airways (microaspiration), GER exacerbates respiratory diseases. Aspiration is a well-known risk to be considered when treating patients in intensive care units. Strong genetic correlations have been identified between COVID-19 infection and GERD susceptibility, suggesting a shared genetic basis for both conditions. Nonetheless, even though GERD, extraesophageal reflex, and COVID-19 have a number of significant risk factors and exhibit similar symptoms, the relationship between these illnesses has not yet been examined in depth. This review is the first of its kind to critically examine the association between the COVID-19 epidemic and GER and its associated diseases. The key objective of this work is to promote the creation of prevention plans, treatment plans, and guidelines while also enhancing and optimizing our understanding of the relationship between COVID-19 and GERs.

An immuno-epidemiological model with waning immunity after infection or vaccination

In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immuno-epidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties. The model consists of a system of first order partial differential equations, involving nonlinear integral terms and different transfer velocities. Structurally, the equation may be interpreted as a Fokker-Planck equation for a piecewise deterministic process. However, unlike the usual models, our equation involves nonlocal effects, representing the infectivity of the whole environment. This, together with the presence of different transfer velocities, makes the proved existence of a solution novel and nontrivial. In addition, the asymptotic behavior of the model is analyzed based on the obtained qualitative properties of the solution. An optimal control problem with objective function including the total number of deaths and costs of vaccination is explored. Numerical results describe the dynamic relationship between contact rates and optimal solutions. The approach can contribute to the understanding of the dynamics of immune responses at population level and may guide public health policies.

Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

Changes and interruptions during COVID-19: caregivers of people with brain health challenges-A qualitative analysis

Background

The social and economic challenges of the COVID-19 pandemic greatly impacted people's physical and mental health. The majority of care for individuals with brain health challenges, including dementia and mental illness, is provided by informal family caregivers. The "Coping with Loneliness, Isolation and COVID-19" (CLIC) Global Caregiver Survey 2020 received responses from over 5,000 caregivers across 50 countries of people living with enduring brain and/or physical health conditions.

Aim

This study examined English-speaking caregivers of people with brain health challenges (dementia and mental health conditions) descriptions of changes and interruptions in their ability to provide care in the context of the COVID-19 pandemic.

Materials and methods

Quantitative and qualitative data were collected as part of the large-scale CLIC Global Caregiver Survey. Data from over 900 English language respondents were analyzed using descriptive statistics and thematic content analysis. A multidisciplinary team of clinicians and health policy practitioners participated in team-based qualitative analyses.

Results

The majority of respondents were from the United States (71% USA), female (83%) and care providers to people living with dementia (81%). Respondents reported concerns about their loved one's physical and mental health, the limited access to other caregiving sources and the limited opportunities to maintain personal wellbeing. Practical, social, psychological and emotional impacts affected their ability to offer care. There was clear evidence that the disruption to health and social care services-institutions, day care and home services impacted the ability to offer care.

Discussion

The pandemic may be seen as a catastrophic "event" that negatively impacted lives and livelihoods. A number of the social determinants of health were negatively impacted for the caregivers surveyed during this prolonged period. Caring for caregivers and supportive health and social care interventions are required to maintain the wellbeing of this informal workforce. This study represents the largest, cross-country survey on the impact of the COVID-19 pandemic on caregivers of people with brain health challenges to date; serving as an important resource for support agencies and to inform policy.

The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?

The COVID-19 pandemic has devastated lives and economies around the world. Initially a primary response was locking down parts of the economy to reduce social interactions and, hence, the virus' spread. After vaccines have been developed and produced in sufficient quantity, they can largely replace broad lock downs. This paper explores how lockdown policies should be varied during the year or so gap between when a vaccine is approved and when all who wish have been vaccinated. Are vaccines and lockdowns substitutes during that crucial time, in the sense that lockdowns should be reduced as vaccination rates rise? Or might they be complementary with the prospect of imminent vaccination increasing the value of stricter lockdowns, since hospitalization and death averted then may be permanently prevented, not just delayed? We investigate this question with a simple dynamic optimization model that captures both epidemiological and economic considerations. In this model, increasing the rate of vaccine deployment may increase or reduce the optimal total lockdown intensity and duration, depending on the values of other model parameters. That vaccines and lockdowns can act as either substitutes or complements even in a relatively simple model casts doubt on whether in more complicated models or the real world one should expect them to always be just one or the other. Within our model, for parameter values reflecting conditions in developed countries, the typical finding is to ease lockdown intensity gradually after substantial shares of the population have been vaccinated, but other strategies can be optimal for other parameter values. Reserving vaccines for those who have not yet been infected barely outperforms simpler strategies that ignore prior infection status. For certain parameter combinations, there are instances in which two quite different policies can perform equally well, and sometimes very small increases in vaccine capacity can tip the optimal solution to one that involves much longer and more intense lockdowns.

Impact of a COVID-19-Related Lockdown on the Experience of Informal Caregiving in Singapore

INTRODUCTION

Lockdowns, while limiting COVID-19 transmission, can affect provision of care by informal caregivers and their caregiving experience. We assessed, among informal caregivers in Singapore, (a) the perceived impact of a 2-month (April to May 2020) nationwide lockdown on their care provision, (b) correlates of different perceptions of the impact of the lockdown on care provision, and (c) association of different perceptions of the impact with negative and positive experiences of caregiving.

METHODS

In the August 2020 wave of the Singapore Life Panel (SLP; nationally representative, longitudinal monthly survey of Singapore citizens and permanent residents aged 50-70 years at baseline), 1,094 participants identified as informal caregivers reported whether their care provision became easier, remained the same, or became harder during the lockdown, compared to before the lockdown. We used multinomial logistic regression to assess the association of caregiver, care recipient, and caregiving context characteristics with their perceptions. Linear regression models examined the association of their perceptions with negative and positive experience domains of the modified Caregiver Reaction Assessment.

RESULTS

Just over one-third (36.1%) of the informal caregivers reported that their care provision became harder during the lockdown compared to before the lockdown. However, nearly one-fifth (18.0%) said that it became easier, and the rest (45.9%) said that it remained the same. Care provision was more likely to be perceived as having become harder among caregivers who were male, of Chinese ethnicity, in worse health, whose care recipients had functional limitations, who did not have caregiving support from cohabiting family members before the lockdown, and who had caregiving support from non-cohabiting family members before the lockdown. The perception that care provision became easier was less likely among caregivers who were of higher age, were unemployed, were socially isolated, and whose care recipients had functional limitations. Caregivers who perceived that care provision became harder during the lockdown were worse-off in negative experiences of caregiving.

CONCLUSION

A nationwide lockdown did not make care provision harder for all informal caregivers. However, informal caregivers for whom it did were more likely to have greater negative experiences of caregiving. The heterogeneity of the impact of lockdowns and the possibility of offering flexibility to non-cohabiting family members who support caregiving should be important considerations when planning for such disruptions.

Exploring the relationship between government stringency and preventative social behaviours during the COVID-19 pandemic in the United Kingdom

We constructed a preventive social behaviours (PSB) Index using survey questions that were aligned with WHO recommendations, and used linear regression to assess the impact of reported COVID-19 deaths (RCD), people's confidence of government handling of the pandemic (CGH) and government stringency (GS) in the United Kingdom (UK) over time on the PSB index. We used repeated, nationally representative, cross-sectional surveys in the UK over the course of 41 weeks from 1st April 2020 to January 28th, 2021, including a total of 38,092 participants. The PSB index was positively correlated with the logarithm of RCD (R: 0.881, p < .001), CGH (R: 0.592, p < .001) and GS (R: 0.785, p < .001), but was not correlated with time (R: -0.118, p = .485). A multivariate linear regression analysis suggests that the log of RCD (coefficient: 0.125, p < .001), GS (coefficient: 0.010, p = .019), and CGH (coefficient: 0.0.009, p < .001) had a positive and significant impact on the PSB Index, while time did not affect it significantly. These findings suggest that people's behaviours could have been affected by multiple factors during the pandemic, with the number of COVID-19 deaths being the largest contributor towards an increase in protective behaviours in our model.

The interplay of social constraints and individual variation in risk tolerance in the emergence of superspreaders

Individual host behaviours can drastically impact the spread of infection through a population. Differences in the value individuals place on both socializing with others and avoiding infection have been shown to yield emergent homophily in social networks and thereby shape epidemic outcomes. We build on this understanding to explore how individuals who do not conform to their social surroundings contribute to the propagation of infection during outbreaks. We show how non-conforming individuals, even if they do not directly expose a disproportionate number of other individuals themselves, can become functional superspreaders through an emergent social structure that positions them as the functional links by which infection jumps between otherwise separate communities. Our results can help estimate the potential success of real-world interventions that may be compromised by a small number of non-conformists if their impact is not anticipated, and plan for how best to mitigate their effects on intervention success.

Opening of hotels and ski facilities: Impact on mobility, spending, and Covid-19 outcomes

This paper investigates how reopening hotels and ski facilities in Poland impacted tourism spending, mobility, and COVID-19 outcomes. We used administrative data from a government program that subsidizes travel to show that the policy increased the consumption of tourism services in ski resorts. By leveraging geolocation data from Facebook, we showed that ski resorts experienced a significant influx of tourists, increasing the number of local users by up to 50%. Furthermore, we confirmed an increase in the probability of meetings between pairs of users from distanced locations and users from tourist and non-tourist areas. As the policy impacted travel and gatherings, we then analyzed its effect on the diffusion of COVID-19. We found that counties with ski facilities experienced more infections after the reopening. Moreover, counties strongly connected to the ski resorts during the reopening had more subsequent cases than weakly connected counties.

Optimal timing of non-pharmaceutical interventions during an epidemic

In response to the recent outbreak of the SARS-CoV-2 virus governments have aimed to reduce the virus's spread through, inter alia, non-pharmaceutical intervention. We address the question when such measures should be implemented and, once implemented, when to remove them. These issues are viewed through a real-options lens and we develop an SIRD-like continuous-time Markov chain model to analyze a sequence of options: the option to intervene and introduce measures and, after intervention has started, the option to remove these. Measures can be imposed multiple times. We implement our model using estimates from empirical studies and, under fairly general assumptions, our main conclusions are that: (1) measures should be put in place not long after the first infections occur; (2) if the epidemic is discovered when there are many infected individuals already, then it is optimal never to introduce measures; (3) once the decision to introduce measures has been taken, these should stay in place until the number of susceptible or infected members of the population is close to zero; (4) it is never optimal to introduce a tier system to phase-in measures but it is optimal to use a tier system to phase-out measures; (5) a more infectious variant may reduce the duration of measures being in place; (6) the risk of infections being brought in by travelers should be curbed even when no other measures are in place. These results are robust to several variations of our base-case model.

Path integral control of a stochastic multi-risk SIR pandemic model

In this paper a Feynman-type path integral control approach is used for a recursive formulation of a health objective function subject to a fatigue dynamics, a forward-looking stochastic multi-risk susceptible-infective-recovered (SIR) model with risk-group's Bayesian opinion dynamics toward vaccination against COVID-19. My main interest lies in solving a minimization of a policy-maker's social cost which depends on some deterministic weight. I obtain an optimal lock-down intensity from a Wick-rotated Schrödinger-type equation which is analogous to a Hamiltonian-Jacobi-Bellman (HJB) equation. My formulation is based on path integral control and dynamic programming tools facilitates the analysis and permits the application of algorithm to obtain numerical solution for pandemic control model.

Intervention uncertainty, household health, and pandemic

This study builds a policy choice model wherein household health status responds to the lockdown during the COVID-19 pandemic. Considering an exogenous policy-decision date, the model implies that the government should maintain the current policy if the perceived effects on infection are below a certain threshold. Specifically, the threshold is determined by policy uncertainty and household concerns regarding health service provision, which further controls the announcement effects of the lockdown. Higher policy uncertainty and concerns regarding health services will diminish the positive impact of the lockdown on household health status.

Optimal vaccination strategies using a distributed model applied to COVID-19

Optimal distribution of vaccines to achieve high population immunity levels is a desirable aim in infectious disease epidemiology. A distributed optimal control epidemiological model that accounts for vaccination was developed and applied to the case of the COVID-19 pandemic. The model proposed here is nonstandard and takes into account the heterogeneity of the infected sub-population with respect to the time since infection, which is essential in the case of COVID-19. Based on the epidemiological characteristics of COVID-19 we analyze several vaccination scenarios and an optimal vaccination policy. In particular we consider random vaccination over the whole population and the prioritization of age groups such as the elderly and compare the effects with the optimal solution. Numerical results of the model show that random vaccination is efficient in reducing the overall number of infected individuals. Prioritization of the elderly leads to lower mortality though. The optimal strategy in terms of total deaths is early prioritization of those groups having the highest contact rates.

Designing an optimal sequence of non-pharmaceutical interventions for controlling COVID-19

The COVID-19 pandemic has had an unprecedented impact on global health and the economy since its inception in December, 2019 in Wuhan, China. Non-pharmaceutical interventions (NPI) like lockdowns and curfews have been deployed by affected countries for controlling the spread of infections. In this paper, we develop a Mixed Integer Non-Linear Programming (MINLP) epidemic model for computing the optimal sequence of NPIs over a planning horizon, considering shortages in doctors and hospital beds, under three different lockdown scenarios. We analyse two strategies - centralised (homogeneous decisions at the national level) and decentralised (decisions differentiated across regions), for two objectives separately - minimization of infections and deaths, using actual pandemic data of France. We linearize the quadratic constraints and objective functions in the MINLP model and convert it to a Mixed Integer Linear Programming (MILP) model. A major result that we show analytically is that under the epidemic model used, the optimal sequence of NPIs always follows a decreasing severity pattern. Using this property, we further simplify the MILP model into an Integer Linear Programming (ILP) model, reducing computational time up to 99%. Our numerical results show that a decentralised strategy is more effective in controlling infections for a given severity budget, yielding up to 20% lesser infections, 15% lesser deaths and 60% lesser shortages in healthcare resources. These results hold without considering logistics aspects and for a given level of compliance of the population.

The macroeconomic implications of disease pandemics in developing countries: An application of Covid-19 in Uganda

This study examines the economy-wide implications of infectious diseases, taking the case of the Covid-19 pandemic in Uganda. Covid-19 containment measures generated social and economic consequences. We employ a recursive dynamic computable general equilibrium model to evaluate the implications on the economy. We design scenarios to mimic the containment policies via labour supply, labour productivity, government healthcare spending and remittance inflows. Results indicate that growth in sector output declines when compared to the no-Covid-19 baseline. However, export growth rates are predicted to be higher. Increased government healthcare spending induces expansion in the healthcare output, but the sectors that produce the intermediate inputs for healthcare production do not grow in tandem. Household welfare declines, and the loss is largest among the top quintile households in both rural and urban areas. Policymakers should revisit Uganda's industrial policy towards domestic production of intermediate inputs to critical domestic sectors such as healthcare. Also, accelerate rural infrastructure development particularly the road network, to facilitate an integrated rural economy induced by the shift in labour and enterprise towards rural areas.

Mitigating virus spread through dynamic control of community-based social interactions for infection rate and cost

The emergence of a new virus in a community may cause significant overload on health services and may spread out to other communities quickly. Social distancing may help reduce the infection rate within a community and prevent the spread of the virus to other communities. However, social distancing comes at a cost; how to strike a good balance between reduction in infection rate and cost of social distancing may be a challenging problem. In this paper, this problem is formulated as a bi-objective optimization problem. Assuming that in a community-based society interaction links have different capacities, the problem is how to determine link capacity to achieve a good trade-off between infection rate and the costs of social distancing restrictions. A standard epidemic model, Susceptible-Infected-Recovered, is extended to model the spread of a virus in the communities. Two methods are proposed to determine dynamically the extent of contact restriction during a virus outbreak. These methods are evaluated using two synthetic networks; the experimental results demonstrate the effectiveness of the methods in decreasing both infection rate and social distancing cost compared to naive methods.

Analysis of optimal lockdown in integral economic-epidemic model

We analyze the optimal lockdown in an economic-epidemic model with realistic infectiveness distribution. The model is described by Volterra integral equations and accurately depicts the COVID-19 infectivity pattern from clinical data. A maximum principle is derived, and a qualitative dynamic analysis of the optimal lockdown problem is provided over finite and infinite horizons. We analytically prove and economically justify the possibility of an endemic scenario when the infection rate begins to climb after the lockdown ends.

Should the COVID-19 lockdown be relaxed or intensified in case a vaccine becomes available?

Immediately after the start of the COVID-19 pandemic in Early 2020, most affected countries reacted with strict lockdown to limit the spread of the virus. Since that time, the measures were adapted on a short time basis according to certain numbers (i.e., number of infected, utilization of intensive care units). Implementing a long-term optimal strategy was not possible since a forecast when R&D will succeed in developing an effective vaccination was not available. Our paper closes this gap by assuming a stochastic arrival rate of the COVID-19 vaccine with the corresponding change in the optimal policy regarding the accompanying optimal lockdown measures. The first finding is that the lockdown should be intensified after the vaccine approval if the pace of the vaccination campaign is rather slow. Secondly, the anticipation of the vaccination arrival also leads to a stricter lockdown in the period without vaccination. For both findings, an intuitive explanation is offered.

An optimal control policy in fighting COVID-19 and infectious diseases

When an outbreak starts spreading, policymakers have to make decisions that affect the health of their citizens and the economy. Some might induce harsh measures, such as a lockdown. Following a long, harsh lockdown, the recession forces policymakers to rethink reopening. To provide an effective strategy, here we propose a control strategy model. Our model assesses the trade-off between social performance and limited medical resources by determining individuals' propensities. The proposed strategy also helps decision-makers to find optimal lockdown and exit strategies for each region. Moreover, the financial loss is minimized. We use the public sentiment information during the pandemic to determine the percentage of individuals with high-risk behavior and the percentage of individuals with low-risk behavior. Hence, we propose an online platform using fear-sentiment information to estimate the personal protective equipment (PPE) burn rate overtime for the entire population. In addition, a study of a COVID-19 dataset for Los Angeles County is performed to validate our model and its results. The total social cost reduces by 18% compared with a control strategy where susceptible individuals are assumed to be homogeneous. We also reduce the total social costs by 26% and 22% compared to other strategies that consider the health-care cost or the social performance cost, respectively.

Chasing up and locking down the virus: Optimal pandemic interventions within a network

During the COVID-19 pandemic countries invested significant amounts of resources into its containment. In early stages of the pandemic most of the (nonpharmaceutical) interventions can be classified into two groups: (i) testing and identification of infected individuals, (ii) social distancing measures to reduce the transmission probabilities. Furthermore, both groups of measures may, in principle, be targeted at certain subgroups of a networked population. To study such a problem, we propose an extension of the SIR model with additional compartments for quarantine and different courses of the disease across several network nodes. We develop the structure of the optimal allocation and study a numerical example of three symmetric regions that are subject to an asymmetric progression of the disease (starting from an initial hotspot). Key findings include that (i) for our calibrations policies are chosen in a "flattening-the-curve," avoiding hospital congestion; (ii) policies shift from containing spillovers from the hotspot initially to establishing a symmetric pattern of the disease; and (iii) testing that can be effectively targeted allows to reduce substantially the duration of the disease, hospital congestion and the total cost, both in terms of lives lost and economic costs.

Ambiguity in a pandemic recession, asset prices, and lockdown policy

Using an asset pricing model of a multisector production economy including pandemic disaster, we explain the average stock price boom and significant cross-sectional variation of stock returns in the United States and Japan during the COVID-19 pandemic recession. We find that two features of the pandemic, namely ambiguity and sector-specific shocks, are critical determinants of the unusual asset price dynamics observed. Extending the model, we analyze the welfare effects of lockdown policy during pandemics for heterogeneous households. We theoretically show that enforcing a lockdown improves the welfare of asset holders and households working in sectors with positive sector-specific shocks. Consequently, a Pareto-optimal lockdown policy controls for the tightness of lockdown to maximize the welfare of households working in sectors with negative sector-specific shocks.

Stability Analysis of an Eight Parameter SIR-Type Model Including Loss of Immunity, and Disease and Vaccination Fatalities

We revisit here a landmark five-parameter SIR-type model, which is maybe the simplest example where a complete picture of all cases, including non-trivial bistability behavior, may be obtained using simple tools. We also generalize it by adding essential vaccination and vaccination-induced death parameters, with the aim of revealing the role of vaccination and its possible failure. The main result is Theorem 1, which describes the stability behavior of our model in all possible cases.

The Economic Effects of COVID-19 Containment Measures

This paper examines the economic effects of COVID-19 containment measures using daily global data on containment measures, infections, and economic activity indicators, such as Nitrogen Dioxide (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{NO}}_{2})$$\end{document}NO2) emissions, international and domestic flights, energy consumption, maritime trade, and mobility indices. Results suggest that containment measures had a significant impact on economic activity—equivalent to about a 10 percent loss in industrial production over 30 days following their implementation. Easing of containment measures results in an increase in economic activity, but the effect is lower (in absolute value) to that of tightening. Fiscal measures used to mitigate the crisis were effective in partly offsetting these costs. We also find that school closures and cancellation of public events are among the most effective measures in curbing infections and are associated with low economic costs. Other highly effective measures like workplace closures and international travel restrictions are among the costliest in economic terms.

Seesaw scenarios of lockdown for COVID-19 pandemic: Simulation and failure analysis

The ongoing COVOD-19(SARS-CoV-2) outbreak has had a devastating impact on the economy, education and businesses. In this paper, the behavior of an epidemic is simulated on different contact networks. Herein, it is assumed that the infection may be transmitted at each contact from an infected person to a susceptible individual with a given probability. The probability of transmitting the disease may change due to the individuals' social behavior or interventions prescribed by the authorities. We utilized simulation on the contact networks to demonstrate how seesaw scenarios of lockdown can curb infection and level the pandemic without maximum pressure on the poor societies. Soft scenarios consist of closing businesses 2, 3, and 4 days in between with four levels of lockdown respected by 25%, 50%, 75%, and 100% of the population. The findings reveal that the outbreak can be flattened under softer alternatives instead of a doomsday scenario of complete lockdown. More specifically, it is turned out that proposed soft lockdown strategies can flatten up to 120% of the pandemic course. It is also revealed that transmission probability has a crucial role in the course of the infection, growth rate of the infection, and the number of infected individuals.

A Review of Matrix SIR Arino Epidemic Models

Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number R has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for (x,y,z) models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity Y(t) which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies.

Mortality containment vs. Economics Opening: Optimal policies in a SEIARD model

We extend the classic approach (SIR) to a SEAIRD model with policy controls. A social planner's objective reflects the trade-off between mortality reduction and GDP, featuring its perception of the value of statistical life (PVSL). We introduce realistic and drastic limitations to the control available to it. Within this setup, we explore the results of various control policies. We notably describe the joint dynamics of infection and economy in different contexts with unique or multiple confinement episodes. Compared to other approaches, our contributions are: (i) to restrict the class of functions accessible to the social planner, and in particular to impose that they remain constant over some fixed periods; (ii) to impose implementation frictions, e.g. a lag in their implementation; (iii) to prove the existence of optimal strategies within this set of possible controls; iv) to exhibit a sudden change in optimal policy as the statistical value of life is raised, from laissez-faire to a sizeable lockdown level, indicating a possible reason for conflicting policy proposals.