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Mathematics of a single-locus model for assessing the impacts of pyrethroid resistance and temperature on population abundance of malaria mosquitoes

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Infectious Disease Modelling 2022年第3期7卷 277-316页

作者： Samantha J.brozak Jemal Mohammed-Awel abba b.gumel School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZ85287USA Department of Mathematics Morgan State UniversityBaltimoreMD21251USA Department of Applied Mathematics University of WaterlooWaterlooOntarioCanada Department of Mathematics and Applied Mathematics University of PretoriaPretoria0002South Africa

This study presents a genetic-ecology modeling framework for assessing the combined impacts of insecticide resistance,temperature variability,and insecticide-based interventions on the population abundance and control of malaria mosquitoes by genotype.Rigorous analyses of the model we developed reveal that the boundary equilibrium with only mosquitoes of homozygous sensitive(resistant)genotype is locally-asymptotically stable whenever a certain ecological threshold,denoted by R^(SS)_(0) eR^(RR)_(0) T,is less than one.Furthermore,genotype i drives genotype j to extinction whenever R j 0>1 and R i 0bits the phenomenon of bistability when both thresholds are less than one.In such a bistable situation,convergence to any of the two boundary equilibria depends on the initial allele distribution in the state variables of the model.Furthermore,in this bistable case,where maxfR^(SS)_(0);R^(RR)_(0)gbasin of attraction of the boundary equilibrium of the mosquito genotype with lower value of the ecological threshold is larger.Specifically,the basin of attraction of the boundary equilibrium for genotype i is larger than that of genotype j if R^(i)_(0)both ecological thresholds exceed one eminfR^(SS)_(0);R^(RR)_(0)g>1T,the two boundary equilibria lose their stability,and a coexistence equilibrium(where all three mosquito genotypes coexist)becomes locally-asymptotically stable.Global sensitivity analysis shows that the key parameters that greatly influence the dynamics and population abundance of resistant mosquitoes include the proportion of new adult mosquitoes that are females,the insecticide-induced mortality rate of adult female mosquitoes,the coverage level and efficacy of adulticides used in the community,the oviposition rates for eggs of heterozygous and homozygous resistant genotypes,and the modification parameter accounting for the reduction in insecticide-induced mortality due to resistance.Numerical simulations show that the adult mosquito popu

关键词： Malaria Insecticide resistance Genotype Pyrethroid Equilibria Population genetics

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Mathematics of dengue transmission dynamics:Roles of vector vertical transmission and temperature fluctuations

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Infectious Disease Modelling 2018年第1期3卷 266-292页

作者： Rahim Taghikhani abba b.gumel School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZUSA

A new deterministic model is designed and used to gain insight into the effect of seasonal variations in temperature and vector vertical transmission on the transmission dynamics of dengue disease.The model,which incorporates(among many other features)the dynamics of the immature dengue-competent mosquitoes,vertical transmission in the vector population,density-dependent larval mortality and temperature effects,is rigorously analysed and simulated using data relevant to the disease dynamics in Chiang Mai province of Thailand.The non-trivial disease-free equilibrium of the model is shown to be globallyasymptotically stable when the associated basic reproduction number of the model is less than unity.Numerical simulations of the model,using data relevant to the disease dynamics in the Chiang Mai province of Thailand,show that vertical transmission in the vector population has only marginal impact on the disease dynamics,and that the effect of vertical transmission is temperature-dependent(in particular,the effect of vertical transmission on the disease dynamics increases for values of the mean monthly temperature in the range[16-28]℃,and decreases with increasing mean monthly temperature thereafter).It is further shown that dengue burden(as measured in terms of disease incidence)is maximized when the mean monthly temperature is in the range[26-28]℃(and dengue burden decreases for mean monthly temperature values above 28℃).Thus,this study suggests that anti-dengue control efforts should be intensified during the period when this temperature range is recorded in the Chiang Mai province(this occurs between June and August).

关键词： Dengue Vertical transmission Temperature Stability Reproduction number

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Modeling the impact of quarantine during an outbreak of Ebola virus disease

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Infectious Disease Modelling 2019年第1期4卷 12-27页

作者： Attila Dénes abba b.gumel bolyai Institute University of SzegedAradi vertanúk tere 1.Szeged H-6720Hungary School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZ 85287-1804USA Other affliation:Department of Mathematics and Applied Mathematics University of PretoriaPretoria 0002South Africa

The quarantine of people suspected of being exposed to an infectious agent is one of the most basic public health measure that has historically been used to combat the spread of communicable diseases in human communities.This study presents a new deterministic model for assessing the population-level impact of the quarantine of individuals suspected of being exposed to disease on the spread of the 2014e2015 outbreaks of Ebola viral disease.It is assumed that quarantine is imperfect(i.e.,individuals can acquire infection during quarantine).In the absence of quarantine,the model is shown to exhibit global dynamics with respect to the disease-free and its unique endemic equilibrium when a certain epidemiological threshold(denoted byR 0)is either less than or greater than unity.Thus,unlike the full model with imperfect quarantine(which is known to exhibit the phenomenon of backward bifurcation),the version of the model with no quarantine does not undergo a backward bifurcation.Using data relevant to the 2014e2015 Ebola transmission dynamics in the three West African countries(Guinea,Liberia and Sierra Leone),uncertainty analysis of the model show that,although the current level and effectiveness of quarantine can lead to significant reduction in disease burden,they fail to bring the associated quarantine reproduction number(R Q0)to a value less than unity(which is needed to make effective disease control or elimination feasible).This reduction of R Q0 is,however,very possible with a modest increase in quarantine rate and effectiveness.It is further shown,via sensitivity analysis,that the parameters related to the effectiveness of quarantine(namely the parameter associated with the reduction in infectiousness of infected quarantined individuals and the contact rate during quarantine)are the main drivers of the disease transmission dynamics.Overall,this study shows that the singular implementation of a quarantine intervention strategy can lead to the effective control or elimination of Ebola viral disease in a communit

关键词： Ebola virus disease Quarantine Global dynamics

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Will vaccine-derived protective immunity curtail COVID-19 variants in the US?

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Infectious Disease Modelling 2021年第1期6卷 1110-1134页

作者： Marina Mancuso Steffen E.Eikenberry abba b.gumel Arizona State University School of Mathematical and Statistical SciencesTempeAZ85287USA Department of Mathematics and Applied Mathematics University of PretoriaPretoria0002South Africa

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 wildtype,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 experienc

关键词： COVID-19 Vaccine Wild-type Variant Reproduction number Herd immunity

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Mathematical analysis of a model for zoonotic visceral leishmaniasis

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Infectious Disease Modelling 2017年第4期2卷 455-474页

作者： Nafiu Hussaini Kamaldeen Okuneye abba b.gumel Department of Mathematical Sciences Bayero University KanoP.M.B.3011KanoNigeria School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZ 85287USA

Zoonotic visceral leishmaniasis(ZVL),caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoirhosts by female sandflies,is endemic inmany parts of the world(notably in Africa,Asia and the Mediterranean).This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations.The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models.In the absence of such phenomenon(which is shown to arise due to the disease-induced mortality in the host populations),the nontrivial disease-free equilibrium of the model is shown to be globallyasymptotically stable when the associated reproduction number of the model is less than unity.Using case and demographic data relevant to ZVL dynamics in Arac atubamunicipality of brazil,it is shown,for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts,that the associated reproduction number of the model (ℛ0) ranges from 0.3 to 1.4,with a mean of ℛ0=0:85.Furthermore,when the effect of such drug treatment is explicitly incorporated in the model(i.e.,accounting for the additional larval and sandfly mortality,following feeding on the treated reservoirs),the range ofℛ0 decreases toℛ02∈[0.1,0.6],with a mean ofℛ0=0:35(this significantly increases the prospect of the effective control or eliminationof the disease).Thus,ZVL transmissionmodels(in communities where such treatment strategy is implemented)that do not explicitly incorporate the effect of such treatmentmay be over-estimating the disease burden(asmeasured in terms ofℛ0)in the community.It is shown thatℛ0 ismore sensitive to increases in sandflylifespanthan thatof the animal reservoir(so,a strategy that focuses on reducing sandflies,rather than the animal reservoir(e.g.,via culling),may be more effective in reducing ZVL burden in the community).Further sensitivity analysis of themodel ranks the sandfly removal rate(by

关键词： Leishmania infantum Zoonotic visceral leishmaniasis(ZVL) Reproduction number Stability backward bifurcation

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

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Infectious Disease Modelling 2020年第1期5卷 510-524页

作者： Enahoro A.Iboi Calistus N.Ngonghala abba b.gumel School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZ85287USA Department of Mathematics University of FloridaGainesvilleFL32611USA Department of Mathematics and Applied Mathematics University of PretoriaPretoria0002South Africa Department of Mathematics Spelman CollegeAtlantaGeorgia30314USA

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,contact tracing and testing,have been quite effective in curtailing and mitigating the burden of the pandemic,it is universally believed that the use of a vaccine may be necessary to effectively curtail and eliminating COVID-19 in human populations.This study is based on the use of a mathematical model for assessing the impact of a hypothetical imperfect anti-COVID-19 vaccine on the control of COVID-19 in the United States.An analytical expression for the minimum percentage of unvaccinated susceptible individuals needed to be vaccinated in order 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 COVID-19 mortality data for the U.S.,show that,for an anti-COVID-19 vaccine with an assumed protective efficacy of 80%,at least 82%of the susceptible US population need to be vaccinated to achieve the herd immunity threshold.The prospect of COVID-19 elimination in the US,using the hypothetical vaccine,is greatly enhanced if the vaccination program is combined with other interventions,such as face mask usage and/or social distancing.Such combination of strategies significantly reduces the level of the vaccine-induced herd immunity threshold needed to eliminate the pandemic in the US.For instance,the herd immunity threshold decreases to 72%if half of the US population regularly wears face masks in public(the threshold decreases to 46%if everyone w

关键词： COVID-19 SARS-CoV-2 Vaccination Social distancing Non-pharmaceutical intervention

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

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Infectious Disease Modelling 2021年第1期6卷 1173-1201页

作者： Samantha J.brozak binod Pant Salman Safdar abba b.gumel School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZ85287USA Department of Mathematics and Applied Mathematics University of PretoriaPretoria0002South Africa

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 neighbor,Pakistan.The base model was rigorously analyzed and 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 non-pharmaceutical interventions).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.This downward trend will be reversed,and India will be recording mild outbreaks,if the control and mitigation strategies are relaxed from their current levels.by early September 2021,our simulations suggest that India could record up to 460,000 cumulative deaths under baseline levels of the implemented control strategies,while Pakistan(where the pandemic is comparatively milder)could see over 24,000 cumulative deaths at current mitigation levels.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,with daily mortality in Pakistan peaking in mid-August to mid-September of 2021.Under the respective baseline control scenarios,our simulations show that the backand-forth mobility between India and Pakistan could delay the time-to-elimination of the COVID-19 pandemic in India and Pakistan to November 2022 and July 2022,respectively.

关键词： COVID-19 SARS-CoV-2 Non-pharmaceutical interventions(NPIs) Metapopulation model Residence-time Reproduction number

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Mathematical assessment of the role of vector insecticide resistance and feeding/resting behavior on malaria transmission dynamics:Optimal control analysis

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Infectious Disease Modelling 2018年第1期3卷 301-321页

作者： Jemal Mohammed-Awel Folashade Agusto Ronald E.Mickens abba b.gumel Department of Mathematics Valdosta State UniversityValdostaGA 31698USA Department of Ecology and Evolutionary biology University of KansasLawrenceKS USA Department of Physics Clark Atlanta UniversityAtlantaGA 30314USA School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZ85287USA

The large-scale use of insecticide-treated bednets(ITNs)and indoor residual spraying(IRS),over the last two decades,has resulted in a dramatic reduction of malaria incidence globally.However,the effectiveness of these interventions is now being threatened by numerous factors,such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening(when humans are not protected by the bednets).This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics.A notable feature of the model is that it stratifies the mosquito population in terms of type(wild or resistant to insecticides)and feeding preference(indoor or outdoor).The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial diseasefree equilibrium,the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist).Simulations of the model,using data relevant to malaria transmission dynamics in Ethiopia(a malaria-endemic nation),show that the use of optimal ITNs alone,or in combination with optimal IRS,is more effective than the singular implementation of an optimal IRS-only strategy.Further,when the effect of the fitness cost of insecticide resistance with respect to fecundity(i.e.,assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes)is accounted for,numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease,and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community.

关键词： Malaria Insecticide resistance ITNs IRS Equilibria

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A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations

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Infectious Disease Modelling 2021年第1期6卷 148-168页

作者： abba b.gumel Enahoro A.Iboi Calistus N.Ngonghala Elamin H.Elbasha School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZ85287USA Department of Mathematics Spelman CollegeAtlantaGA30314USA Department of Mathematics University of FloridaGainesvilleFL32611USA Emerging Pathogens Institute University of FloridaGainesvilleFL32610USA Department of Mathematics and Applied Mathematics University of PretoriaPretoria0002South Africa Merck&Co. Inc.2000 Galloping Hill RoadKenilworthNJ07033USA

The novel coronavirus(COVID-19)pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world.It became the most important public health challenge facing mankind since the 1918 Spanish flu pandemic.Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic.This study presents a primer for formulating,analysing and simulating mathematical models for understanding the dynamics of COVID-19.Specifically,we introduce simple compartmental,Kermack-McKendrick-type epidemic models with homogeneously-and heterogeneously-mixed populations,an endemic model for assessing the potential population-level impact of a hypothetical COVID-19 vaccine.We illustrate how some basic non-pharmaceutical interventions against COVID-19 can be incorporated into the epidemic model.A brief overview of other kinds of models that have been used to study the dynamics of COVID-19,such as agent-based,network and statistical models,is also presented.Possible extensions of the basic model,as well as open challenges associated with the formulation and theoretical analysis of models for COVID-19 dynamics,are suggested.

关键词： COVID-19 SARS-CoV-2 Non-pharmaceutical interventions Face mask Reproduction number

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

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Infectious Disease Modelling 2020年第1期5卷 293-308页

作者： Steffen E.Eikenberry Marina Mancuso Enahoro Iboi Tin Phan Keenan Eikenberry Yang Kuang Eric Kostelich abba b.gumel School of Mathematical and Statistical Sciences Arizona State UniversityTempeAZ85287USA

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 communitywide 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 nonpharmaceutical 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 17e45%of projected deaths over two months in New York,while decreasing the peak daily death rate by 34e58%,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:InWashington,where baseline transmission is much less intense,80%adoption of such masks could reduce mortality by 24e65%(and peak deaths 15e69%),compared to 2e9%mortality reduction in New York(peak death reduction 9e18%).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

关键词： Face mask Non-pharmaceutical intervention Cloth mask N95 respirator Surgical mask SARS-CoV-2 COVID-19

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