ABSTRACT
The effectiveness of control interventions against COVID-19 is threatened by the emergence of SARS-CoV-2 variants of concern. We present a mathematical model for studying the transmission dynamics of two of these variants (Delta and Omicron) in the United States, in the presence of vaccination, treatment of individuals with clinical symptoms of the disease and the use of face masks. The model is parameterized and cross-validated using observed daily case data for COVID-19 in the United States for the period from November 2021 (when Omicron first emerged) to March 2022. Rigorous qualitative analysis of the model shows that the disease-free equilibrium of the model is locally-asymptotically stable when the control reproduction number of the model (denoted by [R]c) is less than one. This equilibrium is shown to be globally-asymptotically stable for a special case of the model, where disease-induced mortality is negligible and both vaccine-derived immunity in fully-vaccinated individuals and natural immunity do not wane, when the associated reproduction number is less than one. The epidemiological implication of the latter result is that the combined vaccination-boosting strategy can lead to the elimination of the pandemic if its implementation can bring (and maintain) the associated reproduction number to a value less than one. An analytical expression for the vaccine-derived herd immunity threshold is derived. Using this expression, together with the baseline values of the parameters of the parameterized model, we showed that the vaccine-derived herd immunity can be achieved in the United States (so that the pandemic will be eliminated) if at least 68% of the population is fully-vaccinated with two of the three vaccines approved for use in the United States (Pfizer or Moderna vaccine). Furthermore, this study showed (as of the time of writing in March 2022) that the control reproduction number of the Omicron variant was approximately 3.5 times that of the Delta variant (the reproduction of the latter is computed to be {approx} 0.2782), indicating that Delta had practically died out and that Omicron has competitively-excluded Delta (to become the predominant variant in the United States). Based on our analysis and parameterization at the time of writing of this paper (March 2022), our study suggests that SARS-CoV-2 elimination is feasible by June 2022 if the current baseline level of the coverage of fully-vaccinated individuals is increased by about 20%. The prospect of pandemic elimination is significantly improved if vaccination is combined with a face mask strategy that prioritizes moderately effective and high-quality masks. Having a high percentage of the populace wearing the moderately-effective surgical mask is more beneficial to the community than having low percentage of the populace wearing the highly-effective N95 masks. We showed that waning natural and vaccine-derived immunity (if considered individually) offer marginal impact on disease burden, except for the case when they wane at a much faster rate (e.g., within three months), in comparison to the baseline (estimated to be within 9 months to a year). Treatment of symptomatic individuals has marginal effect in reducing daily cases of SARS-CoV-2, in comparison to the baseline, but it has significant impact in reducing daily hospitalizations. Furthermore, while treatment significantly reduces daily hospitalizations (and, consequently, deaths), the prospects of COVID-19 elimination in the United States are significantly enhanced if investments in control resources are focused on mask usage and vaccination rather than on treatment.
ABSTRACT
India has been the latest global epicenter for COVID-19, a novel coronavirus disease that emerged in China in late 2019. We present a base mathematical model for the transmission dynamics of COVID-19 in India and its neighbour, Pakistan. The base model, which takes the form of a deterministic system of nonlinear differential equations, is parameterized using cumulative COVID-19 mortality data from each of the two countries. The model was used to assess the population-level impact of the control and mitigation strategies implemented in the two countries (notably community lockdowns, use of face masks, and social-distancing). Numerical simulations of the basic model indicate that, based on the current baseline levels of the control and mitigation strategies implemented, the pandemic trajectory in India is on a downward trend (as characterized by the reproduction number of the disease dynamics in India below, but close to, unity). This downward trend will be reversed, and India will be recording mild outbreaks (i.e., pandemic waves), if the control and mitigation strategies are relaxed from their current levels (e.g., relaxed to the extent that the associated community transmission parameters are increased by 20% or 40% from their current baseline values). Our simulations suggest that India could record up to 460,000 cumulative deaths by early September 2021 under the baseline levels of the control strategies implemented (up to 25,000 of the projected deaths could be averted if the control and mitigation measures are strengthened to the extent that the associated community transmission parameters are reduced by 20% from their baseline values). Our simulations show that the pandemic in Pakistan is much milder, with an estimated projected cumulative mortality of about 24,000 by early September 2021 under the baseline scenario. The basic model was extended to assess the impact of back-and-forth mobility between the two countries. Simulations of the resulting metapopulation model show that the burden of the COVID-19 pandemic in Pakistan increases with increasing values of the average time residents of India spend in Pakistan. In particular, it is shown that the India- to-Pakistan mobility pattern may trigger a fourth wave of the pandemic in Pakistan (under certain mobility scenarios), with daily mortality peaking in mid-August to mid-September of 2021. Under the respective baseline control scenarios, our simulations show that the back-and-forth mobility between India and Pakistan could delay the time-to-elimination of the COVID-19 pandemic in the two countries by three to five months (specifically, under the respective baseline scenarios, elimination could be delayed in India and Pakistan to November 2022 and July 2022, respectively).
ABSTRACT
Dynamic models are used to assess the impact of three types of face masks-cloth masks, surgical/procedure masks and respirators-in controlling the COVID-19 pandemic in the United States. We showed that the pandemic would have failed to establish in the US if a nationwide mask mandate, based on using respirators with moderately-high compliance, had been implemented during the first two months of the pandemic. The other mask types would fail to prevent the pandemic from becoming established. When mask usage compliance is low to moderate, respirators are far more effective in reducing disease burden. Using data from the third wave, we showed that the epidemic could be eliminated in the US if at least 40% of the population consistently wore respirators in public. Surgical masks can also lead to elimination, but requires compliance of at least 55%. Daily COVID-19 mortality could be eliminated in the US by June or July 2021 if 95% of the population opted for either respirators or surgical masks from the beginning of the third wave. We showed that the prospect of effective control or elimination of the pandemic using mask-based strategy is greatly enhanced if combined with other nonpharmaceutical interventions (NPIs) that significantly reduce the baseline community transmission. By slightly modifying the model to include the effect of a vaccine against COVID-19 and waning vaccine-derived and natural immunity, this study shows that the waning of such immunity could trigger multiple new waves of the pandemic in the US. The number, severity and duration of the projected waves depend on the quality of mask type used and the level of increase in the baseline levels of other NPIs used in the community during the onset of the third wave of the pandemic in the US. Specifically, no severe fourth or subsequent wave of the pandemic will be recorded in the US if surgical masks or respirators are used, particularly if the mask-use strategy is combined with an increase in the baseline levels of other NPIs. This study further emphasizes the role of human behavior towards masking on COVID-19 burden, and highlights the urgent need to maintain a healthy stockpile of highly-effective respiratory protection, particularly respirators, to be made available to the general public in times of future outbreaks or pandemics of respiratory diseases that inflict severe public health and socio-economic burden on the population. Author summaryWe developed and used dynamic models to assess the role of highly-effective face coverings on the control and mitigation of the COVID-19 pandemic in the US. The study indicates that implementing and sustaining mask mandates is useful in containing diseases like COVID-19. Additionally, the study suggests that prioritizing the use of respirators is more effective in combating the disease than using other mask types. Specifically, the COVID-19 pandemic would have been prevented from being established in the US if four in every five Americans started wearing respirators during the first two months of the pandemic. The study further shows that COVID-19 can be eliminated in the US if a universal masking strategy that emphasizes respirators, requiring only 23% compliance, is combined with other nonpharmaceutical interventions that can reduce community transmission by 20%. Furthermore, the daily COVID-19 death rate can be completely suppressed by June 2021 if 95% of the population consistently use respirators. The elimination will extend to January 2022 if cloth masks were adopted instead. We conclude that stockpiling and distributing highly-efficient face coverings, notably respirators, will be vital in effectively curtailing future epidemics and pandemics of respiratory diseases.
ABSTRACT
It has been suggested, without rigorous mathematical analysis, that the classical vaccine-induced herd immunity threshold (HIT) assuming a homogeneous population can be substantially higher than the minimum HIT obtained when considering population heterogeneities. We investigated this claim by developing, and rigorously analyzing, a vaccination model that incorporates various forms of heterogeneity and compared it with a model of a homogeneous population. By employing a two-group vaccination model in heterogeneous populations, we theoretically established conditions under which heterogeneity leads to different HIT values, depending on the relative values of the contact rates for each group, the type of mixing between groups, relative vaccine efficacy, and the relative population size of each group. For example, under biased random mixing and when vaccinating a given group results in disproportionate prevention of higher transmission per capita, it is optimal to vaccinate that group before vaccinating other groups. We also found situations, under biased assortative mixing assumption, where it is optimal to vaccinate more than one group. We show that regardless of the form of mixing between groups, the HIT values assuming a heterogeneous population are always lower than the HIT values obtained from a corresponding model with a homogeneous population. Using realistic numerical examples and parametrization (e.g., assuming assortative mixing together with vaccine efficacy of 95% and basic reproduction number of 2.5), we demonstrate that the HIT value considering heterogeneity (e.g., biased assortative mixing) is significantly lower (40%) compared with a HIT value of (63%) assuming a homogeneous population.
ABSTRACT
A novel coronavirus emerged in December of 2019 (COVID-19), causing a pandemic that continues to inflict unprecedented public health and economic burden in all nooks and corners of the world. Although the control of COVID-19 has largely focused on the use of basic public health measures (primarily based on using non-pharmaceutical interventions, such as quarantine, isolation, social-distancing, face mask usage and community lockdowns), three safe and highly-effective vaccines (by AstraZeneca Inc., Moderna Inc. and Pfizer Inc., with protective efficacy of 70%, 94.1% and 95%, respectively) have been approved for use in humans since December 2020. We present a new mathematical model for assessing the population-level impact of the three currently-available anti-COVID vaccines that are administered in humans. The model stratifies the total population into two subgroups, based on whether or not they habitually wear face mask in public. The resulting multigroup model, which takes the form of a deterministic system of nonlinear differential equations, is fitted and parametrized using COVID-19 cumulative mortality data for the third wave of the COVID-19 pandemic in the U.S. Conditions for the asymptotic stability of the associated disease-free equilibrium, as well as expression for the vaccine-derived herd immunity threshold, are rigorously derived. Numerical simulations of the model show that the size of the initial proportion of individuals in the masks-wearing group, together with positive change in behaviour from the non-masks wearing group (as well as those in masks-wearing group do not abandon their masks-wearing habit) play a crucial role in effectively curtailing the COVID-19 pandemic in the U.S. This study further shows that the prospect of achieving herd immunity (required for COVID-19 elimination) in the U.S., using any of the three currently-available vaccines, is quite promising. In particular, while the use of the AstraZeneca vaccine will lead to herd immunity in the U.S. if at least 80% of the populace is vaccinated, such herd immunity can be achieved using either the Moderna or Pfizer vaccine if about 60% of the U.S. population is vaccinated. Furthermore, the prospect of eliminating the pandemic in the US in the year 2021 is significantly enhanced if the vaccination program is complemented with nonpharmaceutical interventions at moderate increased levels of compliance (in relation to their baseline compliance). The study further suggests that, while the waning of natural and vaccine-derived immunity against COVID-19 induces only a marginal increase in the burden and projected time-to-elimination of the pandemic, adding the impacts of the therapeutic benefits of the vaccines into the model resulted in a dramatic reduction in the burden and time-to-elimination of the pandemic.
ABSTRACT
The community lockdown measures implemented in the United States from late March to late May of 2020 resulted in a significant reduction in the community transmission of the COVID-19 pandemic throughout the country. However, a number of US states are currently experiencing an alarming post-lockdown resurgence of the pandemic, triggering fears for a devastating second pandemic wave. We designed a mathematical model for addressing the key question of whether or not the universal use of face masks can halt such resurgence (and possibly avert a second wave, without having to undergo another cycle of major community lockdown) in the states of Arizona, Florida, New York and the entire US. Model calibration, using cumulative mortality data for the four jurisdictions during their respective pre-lockdown and lockdown periods, show that pre-symptomatic and asymptomatically-infectious individuals are, by far, the main drivers of the COVID-19 pandemic in each of the jurisdictions. The implication of this result is that detecting and isolating individuals with clinical symptoms of the pandemic alone (even if all of them are found) may not be sufficient to effectively curtail the pandemic. To achieve such control it is crucially-necessary that pre-symptomatic and asymptomatically-infectious individuals are rapidly detected and isolated (and their contacts rapidly traced and tested). Our study highlights the importance of early implementation of the community lockdown measures. In particular, a sizable reduction in the burden of the pandemic would have been recorded in each of the four jurisdictions if the community lockdown measures were implemented a week or two earlier. These reductions are greatly augmented if the early implementation of the lockdown measures was complemented with a public face mask use strategy. It is shown that the pandemic would have been almost completely suppressed from significantly taking off if the lockdown measures were implemented two weeks earlier, and if a sizable percentage of the residents of the four jurisdictions wore face masks during the respective lockdown periods. We simulated the pandemic in the four jurisdictions under three levels of lifting of community lockdown, namely mild, moderate and high. For the scenario where the control measures adopted are at the baseline levels during the lockdown period, our simulations show that the states of Arizona and Florida will record devastating second waves of the pandemic by the end of 2020, while the state of New York and the entire US will record milder second waves. If the level of lifting of lockdown was mild (i.e., only limited community contacts and business activities are allowed, in comparison to the lockdown period), only the state of Florida will experience a second wave. Our study further shows that the severity of the projected second waves depend on the level of lifting of the community lockdown. For instance, the projected second wave for Arizona and Florida will be more severe than their first waves. It is further shown that, for high level of lifting of community lockdown measures, the increased use of face masks after the lockdown period greatly reduces the burden of the pandemic in each jurisdiction. In particular, for this high lockdown lifting scenario, none of the four jurisdictions will experience a second wave if half of their residents wear face masks consistently after their respective lockdown period. A diagnostic testing strategy that increases the maximum detection rate of asymptomatic infected individuals (followed by contact tracing and self-isolation of the detected cases) greatly reduces the burden of the pandemic in all four jurisdictions, particularly if also combined with a universal face mask use strategy. Finally, it is shown that the universal use of face masks in public, with at least moderate level of compliance, could halt the post-lockdown resurgence of COVID-19, in addition to averting the potential for (and severity of) a second wave of the pandemic in each of the four jurisdictions.
ABSTRACT
A novel Coronavirus (COVID-19), caused by SARS-CoV-2, emerged from the Wuhan city of China at the end of 2019, causing devastating public health and socio-economic burden around the world. In the absence of a safe and effective vaccine or antiviral for use in humans, control and mitigation efforts against COVID-19 are focused on using non-pharmaceutical interventions (aimed at reducing community transmission of COVID-19), such as social (physical)-distancing, community lockdown, use of face masks in public, isolation and contact tracing of confirmed cases and quarantine of people suspected of being exposed to COVID-19. We developed a mathematical model for understanding the transmission dynamics and control of COVID-19 in Nigeria, one of the main epicenters of COVID-19 in Africa. Rigorous analysis of the Kermack-McKendrick-type compartmental epidemic model we developed, which takes the form of a deterministic system of nonlinear differential equations, reveal that the model has a continuum of disease-free equilibria which is locally-asymptotically stable whenever a certain epidemiological threshold, called the control reproduction (denoted by [R]c), is less than unity. The epidemiological implication of this result is that the pandemic can be effectively controlled (or even eliminated) in Nigeria if the control strategies implemented can bring (and maintain) the epidemiological threshold ([R]c) to a value less than unity. The model, which was parametrized using COVID-19 data published by Nigeria Centre for Disease Control (NCDC), was used to assess the community-wide impact of various control and mitigation strategies in the entire Nigerian nation, as well as in two states (Kano and Lagos) within the Nigerian federation and the Federal Capital Territory (FCT Abuja). It was shown that, for the worst-case scenario where social-distancing, lockdown and other community transmission reduction measures are not implemented, Nigeria would have recorded a devastatingly high COVID-19 mortality by April 2021 (in hundreds of thousands). It was, however, shown that COVID-19 can be effectively controlled using social-distancing measures provided its effectiveness level is at least moderate. Although the use of face masks in the public can significantly reduce COVID-19 in Nigeria, its use as a sole intervention strategy may fail to lead to the realistic elimination of the disease (since such elimination requires unrealistic high compliance in face mask usage in the public, in the range of 80% to 95%). COVID-19 elimination is feasible in both the entire Nigerian nation, and the States of Kano and Lagos, as well as the FCT, if the public face masks use strategy (using mask with moderate efficacy, and moderate compliance in its usage) is complemented with a social-distancing strategy. The lockdown measures implemented in Nigeria on March 30, 2020 need to be maintained for at least three to four months to lead to the effective containment of COVID-19 outbreaks in the country. Relaxing, or fully lifting, the lockdown measures sooner, in an effort to re-open the economy or the country, may trigger a deadly second wave of the pandemic.
ABSTRACT
The novel coronavirus (COVID-19) that emerged from Wuhan city of China in late December 2019 continue to pose devastating public health and economic challenges across the world. Although the community-wide implementation of basic non-pharmaceutical intervention measures, such as social-distancing, quarantine of suspected COVID-19 cases, isolation of confirmed cases, use of face masks in public, and contact-tracing, have been quite effective in curtailing and mitigating the burden of the pandemic, it is universally believed that the use of an anti-COVID-19 vaccine is necessary to build the community herd immunity needed to effectively control and eliminate the pandemic. This study is based on the design and use of a mathematical model for assessing the population-level impact of a hypothetical imperfect anti-COVID-19 vaccine on the control of COVID-19. An analytical expression for the minimum number of unvaccinated susceptible individuals needed to be vaccinated to achieve vaccine-induced community herd immunity is derived. The epidemiological consequence of the herd immunity threshold is that the disease can be effectively controlled or eliminated if the minimum herd immunity threshold is achieved in the community. Simulations of the model, using baseline parameter values obtained from fitting the model with mortality data relevant to COVID-19 dynamics in the US states of New York and Florida, as well as for the entire US, show that, for an anti-COVID-19 vaccine with an assumed protective efficacy of 80%, the minimum herd immunity threshold for the entire US, state of New York and state of Florida are, respectively, 90%, 84% and 85%. Furthermore, it was shown that, while a significantly large increase in vaccination rate (from baseline) is necessarily needed to eliminate COVID-19 from the entire US, the pandemic can be eliminated from the states of New York and Florida if the vaccination rate is marginally increased (by as low as 10%) from its baseline value. The prospect of COVID-19 elimination in the US or in the two states of New York and Florida is greatly enhanced if the vaccination program is combined with a public mask use program or an effective social-distancing measure. Such combination of strategies significantly reduces the vaccine-induced herd immunity threshold. Finally, it is shown that the vaccination program is more likely to lead to COVID-19 elimination in the state of Florida, followed by the state of New York and then the entire US.
ABSTRACT
A pandemic of a novel Coronavirus emerged in December of 2019 (COVID-19), causing devastating public health impact across the world. In the absence of a safe and effective vaccine or antivirals, strategies for controlling and mitigating the burden of the pandemic are focused on non-pharmaceutical interventions, such as social-distancing, contact-tracing, quarantine, isolation and the use of face-masks in public. We develop a new mathematical model for assessing the population-level impact of the aforementioned control and mitigation strategies. Rigorous analysis of the model shows that the disease-free equilibrium is locally-asymptotically stable if a certain epidemiological threshold, known as the reproduction number (denoted by [R]c), is less than unity. This equilibrium is globally-asymptotically stable, for a special case of the model where quarantined-susceptible individuals do not acquire COVID-19 infection during quarantine, when [R]c is less than unity. The epidemiological consequence of this theoretical result is that, the community-wide implementation of control interventions that can bring (and maintain) [R]c to a value less than unity will lead to the effective control (or elimination) of COVID-19 in the community. Simulations of the model, using data relevant to COVID-19 transmission dynamics in the US state of New York and the entire US, show that the pandemic burden will peak in mid and late April, respectively. The worst-case scenario projections for cumulative mortality (based on baseline levels of interventions) are 105, 100 for New York state and 164, 000 for the entire US by the end of the pandemic. These numbers dramatically decreased by 80% and 64%, respectively, if adherence to strict social-distancing measures is improved and maintained until the end of May or June. The duration and timing of the relaxation or termination of the strict social-distancing measures are crucially-important in determining the future trajectory of the COVID-19 pandemic. This study shows that early termination of the strict social-distancing measures could trigger a devastating second wave with burden similar to those projected before the onset of the strict social-distance measures were implemented. The use of efficacious face-masks (such as surgical masks, with estimated efficacy [≥] 70%) in public could lead to the elimination of the pandemic if at least 70% of the residents of New York state use such masks in public consistently (nationwide, a compliance of at least 80% will be required using such masks). The use of low efficacy masks, such as cloth masks (of estimated efficacy less than 30%), could also lead to significant reduction of COVID-19 burden (albeit, they are not able to lead to elimination). Combining low efficacy masks with improved levels of the other anti-COVID-19 intervention strategies can lead to the elimination of the pandemic. This study emphasizes the important role social-distancing plays in curtailing the burden of COVID-19. Increases in the adherence level of social-distancing protocols result in dramatic reduction of the burden of the pandemic, and the timely implementation of social-distancing measures in numerous states of the US may have averted a catastrophic outcome with respect to the burden of COVID-19. Using face-masks in public (including the low efficacy cloth masks) is very useful in minimizing community transmission and burden of COVID-19, provided their coverage level is high. The masks coverage needed to eliminate COVID-19 decreases if the masks-based intervention is combined with the strict social-distancing strategy.
ABSTRACT
Face mask use by the general public for limiting the spread of the COVID-19 pandemic is controversial, though increasingly recommended, and the potential of this intervention is not well understood. We develop a compartmental model for assessing the community-wide impact of mask use by the general, asymptomatic public, a portion of which may be asymptomatically infectious. Model simulations, using data relevant to COVID-19 dynamics in the US states of New York and Washington, suggest that broad adoption of even relatively ineffective face masks may meaningfully reduce community transmission of COVID-19 and decrease peak hospitalizations and deaths. Moreover, mask use decreases the effective transmission rate in nearly linear proportion to the product of mask effectiveness (as a fraction of potentially infectious contacts blocked) and coverage rate (as a fraction of the general population), while the impact on epidemiologic outcomes (death, hospitalizations) is highly nonlinear, indicating masks could synergize with other non-pharmaceutical measures. Notably, masks are found to be useful with respect to both preventing illness in healthy persons and preventing asymptomatic transmission. Hypothetical mask adoption scenarios, for Washington and New York state, suggest that immediate near universal (80%) adoption of moderately (50%) effective masks could prevent on the order of 17-45% of projected deaths over two months in New York, while decreasing the peak daily death rate by 34-58%, absent other changes in epidemic dynamics. Even very weak masks (20% effective) can still be useful if the underlying transmission rate is relatively low or decreasing: In Washington, where baseline transmission is much less intense, 80% adoption of such masks could reduce mortality by 24-65% (and peak deaths 15-69%), compared to 2-9% mortality reduction in New York (peak death reduction 9-18%). Our results suggest use of face masks by the general public is potentially of high value in curtailing community transmission and the burden of the pandemic. The community-wide benefits are likely to be greatest when face masks are used in conjunction with other non-pharmaceutical practices (such as social-distancing), and when adoption is nearly universal (nation-wide) and compliance is high.
