arXiv subjects

Abba B. Gumel

Publications and source records attributed to Abba B. Gumel.

3 recordsLinked to original sources

arXiv2026

Analytical and numerical methods for spillover effects in prioritized PrEP for HIV prevention

Pre-exposure prophylaxis (PrEP) is an effective intervention for preventing HIV transmission, but high cost and uneven uptake raise challenges for resource allocation. While spillover effects, wherein PrEP use in one group reduces infections in others, are known to occur, they remain poorly quantified and rarely guide policy. We provide a comprehensive modeling study for PrEP spillover across risk groups, and develop analytic and numerical tools for its quantification. We first develop a compartmental model for HIV transmission that stratifies the population into interacting subgroups: heterosexual males (HETM), high- and low-risk heterosexual females (HETF-hi/HETF-lo) and men who have sex with men (MSM). The asymptotic stability of the disease-free equilibrium of the model is analyzed. Spillover is quantified by deriving an expression for the spillover-adjusted number needed to treat (NNT), a measure of the population-level impact of PrEP. Simulations show PrEP delivery to MSM yields substantial indirect benefits, particularly for HETF-lo, where spillover exceeds the direct effect by a factor of five. We show targeting HETF-hi outperforms direct PrEP delivery to HETM, emphasizing the importance of intra-group heterogeneity. To evaluate whether these results hold under more detailed assumptions, we embed our framework into the national HOPE model maintained by the Centers for Disease Control and Prevention (CDC) and conduct global sensitivity analysis using Sobol indices with Polynomial Chaos Expansion. This approach extends our analytical insights and quantifies how uncertainty in PrEP allocation propagates through complex dynamics. Further, this framework provides a numerical procedure for quantifying spillover where direct analysis is impractical. Our results show that spillover is a central driver of PrEP dynamics and that failing to account for it risks mis-allocating resources.

math.DS↗

arXiv2020

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

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.

q-bio.PE↗

arXiv2020

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

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.

q-bio.PE↗