Mathematical assessment of the role of human behavior changes on SARS-CoV-2 transmission dynamics (preprint)

The COVID-19 pandemic has not only presented a major global public health and socio-economic crisis, but has also significantly impacted human behavior towards adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities worldwide. The dynamic nature of the pandemic has prompted extensive changes in individual and collective behaviors towards the pandemic. This study is based on the use of mathematical modeling approaches to assess the extent to which SARS-CoV-2 transmission dynamics is impacted by population-level changes of human behavior due to factors such as (a) the severity of transmission (such as disease-induced mortality and level of symptomatic transmission), (b) fatigue due to the implementation of mitigation interventions measures (e.g., lockdowns) over a long (extended) period of time, (c) social peer-pressure, among others. A novel behavior-epidemiology model, which takes the form of a deterministic system of nonlinear differential equations, is developed and fitted using observed cumulative SARS-CoV-2 mortality data during the first wave in the United States. Rigorous analysis of the model shows that its disease-free equilibrium is locally-asymptotically stable whenever a certain epidemiological threshold, known as the control reproduction number (denoted by[R] C) is less than one, and the disease persists (i.e., causes significant outbreak or outbreaks) if the threshold exceeds one. The model fits the observed data, as well as makes a more accurate prediction of the observed daily SARS-CoV-2 mortality during the first wave (March 2020 -June 2020), in comparison to the equivalent model which does not explicitly account for changes in human behavior. Of the various metrics for human behavior changes during the pandemic considered in this study, it is shown that behavior changes due to the level of SARS-CoV-2 mortality and symptomatic transmission were more influential (while behavioral changes due to the level of fatigue to interventions in the community was of marginal impact). It is shown that an increase in the proportion of exposed individuals who become asymptomatically-infectious at the end of the exposed period (represented by a parameter r) can lead to an increase (decrease) in the control reproduction number ([R]C) if the effective contact rate of asymptomatic individuals is higher (lower) than that of symptomatic individuals. The study identifies two threshold values of the parameter r that maximize the cumulative and daily SARS-CoV-2 mortality, respectively, during the first wave. Furthermore, it is shown that, as the value of the proportion r increases from 0 to 1, the rate at which susceptible non-adherent individuals change their behavior to strictly adhere to public health interventions decreases. Hence, this study suggests that, as more newly-infected individuals become asymptomatically-infectious, the level of positive behavior change, as well as disease severity, hospitalizations and disease-induced mortality in the community can be expected to significantly decrease (while new cases may rise, particularly if asymptomatic individuals have higher contact rate, in comparison to symptomatic individuals).

Mathematical assessment of the role of waning and boosting immunity against the BA.1 Omicron variant in the United States (preprint)

Three safe and effective vaccines against SARS-CoV-2 (the Pfizer-BioNTech, Moderna and Johnson & Johnson vaccines) have played a major role in combating the COVID-19 pandemic in the United States. However, the effectiveness of these vaccines and vaccination programs has been challenged by the emergence of new SARS-CoV-2 variants of concern. A new mathematical model is formulated to assess the population-level impact of the waning and boosting of vaccine-derived and natural immunity against the Omicron variant in the United States. To account for gradual waning of vaccine-derived immunity, we considered three vaccination classes (V1, V2 and V3; where subscripts 1, 2 and 3 represent high, moderate and low levels of immunity, respectively). The disease-free equilibrium of the model was shown to be globally-asymptotically stable, for two special cases, whenever a certain associated epidemiological quantity, known as the vaccination reproduction number of the model, is less than one. The model was fitted using observed daily case data for the Omicron BA.1 variant in the United States. Simulations of the resulting parameterized model showed that, for the case where the high-level of the vaccine-derived protective efficacy received by individuals in the first vaccinated class (V1) is set at its baseline value (85%; while the vaccine-protective efficacy for individuals in the V2 and V3 classes, as well as natural immunity, are maintained at baseline), population-level herd immunity can be achieved in the United States via vaccination-boosting strategy, if at least 59% of the susceptible populace is fully-vaccinated followed by the boosting of about 71.5% of the fully-vaccinated individuals whose vaccine-derived immunity has waned to moderate or low level. However, if the high level of vaccine-induced efficacy for individuals in the V1 class is reduced to 55%, for instance, achieving herd immunity requires fully-vaccinating at least 91% of the susceptible population (followed by marginal boosting of those in whom the vaccine-derived immunity has waned to moderate or low level). In the absence of boosting of vaccine-derived and natural immunity, waning of immunity (both vaccine-derived and natural) only causes a marginal increase in the average number of new cases at the peak of the pandemic. Boosting of both immunity types at baseline could result in a dramatic reduction in the average number of daily new cases at the peak, in comparison to the corresponding waning scenario without boosting of immunity. Furthermore, boosting of vaccine-derived immunity (at baseline) is more beneficial (in reducing the burden of the pandemic) than boosting of natural immunity (at baseline). Specifically, for the fast waning of immunity scenario (where both vaccine-derived and natural immunity are assumed to wane within three months), boosting vaccine-derived immunity at baseline reduces the average number of daily cases at the peak by 90% (in comparison to the corresponding scenario without boosting of the vaccine-derived immunity), whereas boosting of natural immunity (at baseline) only reduced the corresponding peak daily cases (in comparison to the corresponding scenario without boosting of natural immunity) by 62%. It was further shown that boosting of vaccine-derived (implemented near the baseline level) increased the prospects of altering the trajectory of COVID-19 from persistence to possible elimination (even for the fast waning scenario of vaccine-derived immunity). Thus, a vaccination strategy that emphasizes boosting of immunity would significantly enhance the prospects of SARS-CoV-2 elimination in the United States.

Dynamics of the Delta and Omicron variants of SARS-CoV-2 in the United States: the battle of supremacy in the presence of vaccination, mask usage and antiviral treatment (preprint)

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. Using current daily case data for COVID-19, we showed that the predominant Omicron variant can be eliminated if current control measures are maintained at their baseline levels. Vaccine-derived herd immunity can be achieved (so that the pandemic will be eliminated) if at least 68% of the population is fully-vaccinated. We showed that elimination is feasible by June 2022 if current baseline level of full vaccination coverage 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. Further, while treatment significantly reduces hospitalization, the prospects of COVID-19 elimination in the United States is more significantly enhanced if investments in control resources are focused on mask usage and vaccination rather than on treatment.

Unraveling the dynamics of the Omicron and Delta variants of the 2019 coronavirus in the presence of vaccination, mask usage, and antiviral treatment (preprint)

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 ≈ 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.

Will Vaccine-derived Protective Immunity Curtail COVID-19 Variants in the US? (preprint)

ABSTRACT Multiple effective vaccines are currently being deployed to combat the COVID-19 pandemic, and are viewed as the major factor in marked reductions of disease burden in regions with moderate to high vaccination coverage. The effectiveness of COVID-19 vaccination programs is, however, significantly threatened by the emergence of new SARS-COV-2 variants that, in addition to being more transmissible than the wild-type (original) strain, may at least partially evade existing vaccines. A two-strain (one wild-type, one variant) and two-group (vaccinated or otherwise) mechanistic mathematical model is designed and used to assess the impact of the vaccine-induced cross-protective efficacy on the spread the COVID-19 pandemic in the United States. Rigorous analysis of the model shows that, in the absence of any co-circulating SARS-CoV-2 variant, the vaccine-derived herd immunity threshold needed to eliminate the wild-type strain can be achieved if 59% of the US population is fully-vaccinated with either the Pfizer or Moderna vaccine. This threshold increases to 76% if the wild-type strain is co-circulating with the Alpha variant (a SARS-CoV-2 variant that is 56% more transmissible than the wild-type strain). If the wild-type strain is co-circulating with the Delta variant (which is estimated to be 100% more transmissible than the wild-type strain), up to 82% of the US population needs to be vaccinated with either of the aforementioned vaccines to achieve the vaccine-derived herd immunity. Global sensitivity analysis of the model reveal the following four parameters as the most influential in driving the value of the reproduction number of the variant strain (hence, COVID-19 dynamics) in the US: (a) the infectiousness of the co-circulating SARS-CoV-2 variant, (b) the proportion of individuals fully vaccinated (using Pfizer or Moderna vaccine) against the wild-type strain, (c) the cross-protective efficacy the vaccines offer against the variant strain and (d) the modification parameter accounting for the reduced infectiousness of fully-vaccinated individuals experiencing breakthrough infection. Specifically, numerical simulations of the model show that future waves or surges of the COVID-19 pandemic can be prevented in the US if the two vaccines offer moderate level of cross-protection against the variant (at least 67%). This study further suggests that a new SARS-CoV-2 variant can cause a significant disease surge in the US if (i) the vaccine coverage against the wild-type strain is low (roughly < 66%), (ii) the variant is much more transmissible (e.g., 100% more transmissible) than the wild-type strain, or (iii) the level of cross-protection offered by the vaccine is relatively low (e.g., less than 50%). A new SARS-CoV-2 variant will not cause such surge in the US if it is only moderately more transmissible (e.g., the Alpha variant, which is 56% more transmissible) than the wild-type strain, at least 66% of the population of the US is fully vaccinated, and the three vaccines being deployed in the US (Pfizer, Moderna, and Johnson & Johnson) offer a moderate level of cross-protection against the variant.

Assessing the impact of widespread respirator use in curtailing COVID-19 transmission in the United States (preprint)

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 summary We 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.