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 RC) 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 (RC) 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).

Dynamics of COVID-19 pandemic in India and Pakistan: A metapopulation modelling approach (preprint)

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).

Vaccination and herd immunity thresholds in heterogeneous populations (preprint)

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.

Mathematical assessment of the roles of vaccination and non-pharmaceutical interventions on COVID-19 dynamics: a multigroup modeling approach (preprint)

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), a number of exceptionally-promising vaccines are about to be approved for use in humans by the U.S. Food and Drugs Administration. We present a new mathematical model for assessing the population-level impact of the candidate vaccines, particularly for the case where the vaccination program is complemented with a social-distancing control measure at a certain compliance level. 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 compartmental, deterministic system of nonlinear differential equations, is parametrized using COVID-19 cumulative mortality data. Conditions for the asymptotic stability of the associated disease-free equilibrium, as well as expression for the vaccine-derived herd immunity threshold, are derived. This study shows that the prospect of COVID-19 elimination using any of the three candidate vaccines is quite promising, and that such elimination is more feasible if the vaccination program is combined with social-distancing control measures (implemented at moderate to high level of compliance).

Could masks curtail the post-lockdown resurgence of COVID-19 in the US? (preprint)

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.

Mathematical Modeling and Analysis of COVID-19 pandemic in Nigeria (preprint)

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.

Will an imperfect vaccine curtail the COVID-19 pandemic in the U.S.? (preprint)

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.

Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus (preprint)

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 antiviral, 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 Rc), is less than unity. 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 the baseline levels of anti-COVID non-pharmaceutical interventions considered in the study) decrease dramatically by 80% and 64%, respectively, if the strict social-distancing measures implemented are maintained until the end of May or June, 2020. 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-distancing measures were implemented. The use of efficacious face-masks (such as surgical masks, with estimated efficacy greater than or equal to 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.

Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus (preprint)

A novel Coronavirus pandemic emerged in December of 2019, causing devastating public health impact across the world. In the absence of a safe and effective vaccine or antiviral, strategies for 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 these mitigation strategies. Simulations of the model, using data relevant to COVID-19 transmission in New York state and the entire US, show that the pandemic will peak in mid and late April, respectively. The worst-case scenario projections for cumulative mortality (based on the baseline levels of anti-COVID non-pharmaceutical interventions considered in the study) in New York State and the entire US decrease dramatically by 80% and 64%, respectively, if the strict social-distancing measures implemented are maintained until the end of May or June, 2020. This study shows that early termination of strict social-distancing could trigger a devastating second wave with burden similar to that projected before the onset of strict social-distance. The use of efficacious face-masks (efficacy greater than 70%) could lead to the elimination of the pandemic if at least 70% of the residents of New York state use such masks 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 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 other anti-COVID-19 intervention measures can lead to elimination of the pandemic. The mask coverage needed to eliminate COVID-19 decreases if mask-use is combined with strict social-distancing.

To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic (preprint)

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.

To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic (preprint)

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. Masks are found to be useful with respect to both preventing illness in healthy persons and preventing asymptomatic transmission. Hypothetical mask adoption scenarios 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. 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.