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Korsah MA, Johnston ST, Tiedje KE, Day KP, Flegg JA, Walker CR. Mathematical Assessment of the Role of Intervention Programs for Malaria Control. Bull Math Biol 2024; 86:91. [PMID: 38888640 PMCID: PMC11189351 DOI: 10.1007/s11538-024-01321-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2023] [Accepted: 06/03/2024] [Indexed: 06/20/2024]
Abstract
Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.
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Affiliation(s)
- Maame Akua Korsah
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia.
| | - Stuart T Johnston
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Kathryn E Tiedje
- Department of Microbiology and Immunology, Bio21 Institute and Peter Doherty Institute, The University of Melbourne, Melbourne, Australia
| | - Karen P Day
- Department of Microbiology and Immunology, Bio21 Institute and Peter Doherty Institute, The University of Melbourne, Melbourne, Australia
| | - Jennifer A Flegg
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Camelia R Walker
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
- Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia
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Korsah MA, Johnston ST, Tiedje KE, Day KP, Flegg JA, Walker CR. Mathematical assessment of the role of intervention programs for malaria control. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2023:2023.12.18.23300185. [PMID: 38196597 PMCID: PMC10775318 DOI: 10.1101/2023.12.18.23300185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/11/2024]
Abstract
Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.
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Affiliation(s)
- Maame Akua Korsah
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Stuart T Johnston
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Kathryn E Tiedje
- Department of Microbiology and Immunology, Bio21 Institute and Peter Doherty Institute, The University of Melbourne, Melbourne, Australia
| | - Karen P Day
- Department of Microbiology and Immunology, Bio21 Institute and Peter Doherty Institute, The University of Melbourne, Melbourne, Australia
| | - Jennifer A Flegg
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Camelia R Walker
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
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Stresman G, DePina AJ, Nelli L, Monteiro DDS, Leal SDV, Moreira AL, Furtado UD, Roka JCL, Neatherlin J, Gomes C, Tfeil AK, Lindblade KA. Factors related to human-vector contact that modify the likelihood of malaria transmission during a contained Plasmodium falciparum outbreak in Praia, Cabo Verde. FRONTIERS IN EPIDEMIOLOGY 2022; 2:1031230. [PMID: 38455281 PMCID: PMC10910924 DOI: 10.3389/fepid.2022.1031230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/29/2022] [Accepted: 11/10/2022] [Indexed: 03/09/2024]
Abstract
Background Determining the reproductive rate and how it varies over time and space (RT) provides important insight to understand transmission of a given disease and inform optimal strategies for controlling or eliminating it. Estimating RT for malaria is difficult partly due to the widespread use of interventions and immunity to disease masking incident infections. A malaria outbreak in Praia, Cabo Verde in 2017 provided a unique opportunity to estimate RT directly, providing a proxy for the intensity of vector-human contact and measure the impact of vector control measures. Methods Out of 442 confirmed malaria cases reported in 2017 in Praia, 321 (73%) were geolocated and informed this analysis. RT was calculated using the joint likelihood of transmission between two cases, based on the time (serial interval) and physical distance (spatial interval) between them. Log-linear regression was used to estimate factors associated with changes in RT, including the impact of vector control interventions. A geostatistical model was developed to highlight areas receptive to transmission where vector control activities could be focused in future to prevent or interrupt transmission. Results The RT from individual cases ranged between 0 and 11 with a median serial- and spatial-interval of 34 days [interquartile range (IQR): 17-52] and 1,347 m (IQR: 832-1,985 m), respectively. The number of households receiving indoor residual spraying (IRS) 4 weeks prior was associated with a reduction in RT by 0.84 [95% confidence interval (CI) 0.80-0.89; p-value <0.001] in the peak-and post-epidemic compared to the pre-epidemic period. Conclusions Identifying the effect of reduced human-vector contact through IRS is essential to determining optimal intervention strategies that modify the likelihood of malaria transmission and can inform optimal intervention strategies to accelerate time to elimination. The distance within which two cases are plausibly linked is important for the potential scale of any reactive interventions as well as classifying infections as imported or introduced and confirming malaria elimination.
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Affiliation(s)
- Gillian Stresman
- Department of Infection Biology, London School of Hygiene and Tropical Medicine, London, United Kingdom
- College of Public Health, University of South Florida, Tampa, FL, United States
| | | | - Luca Nelli
- School of Biodiversity, One Health, and Veterinary Medicine, University of Glasgow, Glasgow, United Kingdom
| | | | - Silvânia da Veiga Leal
- Laboratório de Entomologia Médica, Instituto Nacional de Saúde Pública, Praia, Cabo Verde
| | | | | | | | - John Neatherlin
- U.S. Centers for Disease Control and Prevention, Atlanta, GA, United States
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Brozak SJ, Mohammed-Awel J, Gumel AB. Mathematics of a single-locus model for assessing the impacts of pyrethroid resistance and temperature on population abundance of malaria mosquitoes. Infect Dis Model 2022; 7:277-316. [PMID: 35782338 PMCID: PMC9234087 DOI: 10.1016/j.idm.2022.05.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Revised: 05/25/2022] [Accepted: 05/25/2022] [Indexed: 11/18/2022] Open
Abstract
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 R0SS(R0RR), is less than one. Furthermore, genotype i drives genotype j to extinction whenever R0j>1 and R0i<1 (where i, j = SS or RR, with i ≠ j). The model exhibits 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 max{R0SS,R0RR}<1, the basin 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 R0i<R0j<1. When both ecological thresholds exceed one (min{R0SS,R0RR}>1), 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 population increases with increasing temperature until a peak is reached at 31 °C, and declines thereafter. Simulating the model for moderate and high adulticide coverage, together with varying fitness costs of resistance, shows a switch in the dominant genotype at equilibrium as temperature is varied. In other words, this study shows that, for certain combinations of adulticide coverage and fitness costs of insecticide resistance, increases in temperature could result in effective management of resistance (by causing the switch from a stable resistant-only boundary equilibrium (at 18 °C) to a stable sensitive-only boundary equilibrium (at 25 °C)). Finally, this study shows that, for moderate fitness costs of resistance, density-dependent larval mortality suppresses the total population of adult mosquitoes with the resistant allele for all temperature values in the range [18 °C–36 °C].
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Affiliation(s)
- Samantha J. Brozak
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA
| | - Jemal Mohammed-Awel
- Department of Mathematics, Morgan State University, Baltimore, MD, 21251, USA
| | - Abba B. Gumel
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa
- Corresponding author. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA.
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Witbooi P, Abiodun G, Nsuami M. A model of malaria population dynamics with migrants. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:7301-7317. [PMID: 34814250 DOI: 10.3934/mbe.2021361] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We present a compartmental model in ordinary differential equations of malaria disease transmission, accommodating the effect of indoor residual spraying on the vector population. The model allows for influx of infected migrants into the host population and for outflow of recovered migrants. The system is shown to have positive solutions. In the special case of no infected immigrants, we prove global stability of the disease-free equilibrium. Existence of a unique endemic equilibrium point is also established for the case of positive influx of infected migrants. As a case study we consider the combined South African malaria region. Using data covering 31 years, we quantify the effect of malaria infected immigrants on the South African malaria region.
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Affiliation(s)
- Peter Witbooi
- Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South Africa
| | - Gbenga Abiodun
- Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South Africa
| | - Mozart Nsuami
- Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South Africa
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Namias A, Jobe NB, Paaijmans KP, Huijben S. The need for practical insecticide-resistance guidelines to effectively inform mosquito-borne disease control programs. eLife 2021; 10:e65655. [PMID: 34355693 PMCID: PMC8346280 DOI: 10.7554/elife.65655] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 07/26/2021] [Indexed: 11/13/2022] Open
Abstract
Monitoring local mosquito populations for insecticide resistance is critical for effective vector-borne disease control. However, widely used phenotypic assays, which are designed to monitor the emergence and spread of insecticide resistance (technical resistance), do not translate well to the efficacy of vector control products to suppress mosquito numbers in the field (practical resistance). This is because standard testing conditions such as environmental conditions, exposure dose, and type of substrate differ dramatically from those experienced by mosquitoes under field conditions. In addition, field mosquitoes have considerably different physiological characteristics such as age and blood-feeding status. Beyond this, indirect impacts of insecticide resistance and/or exposure on mosquito longevity, pathogen development, host-seeking behavior, and blood-feeding success impact disease transmission. Given the limited number of active ingredients currently available and the observed discordance between resistance and disease transmission, we conclude that additional testing guidelines are needed to determine practical resistance-the efficacy of vector control tools under relevant local conditions- in order to obtain programmatic impact.
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Affiliation(s)
- Alice Namias
- Département de Biologie, Ecole Normale Supérieure, PSL Research University, Paris, France
- Institut des Sciences de l'Evolution de Montpellier (ISEM), Université de Montpellier, CNRS, IRD, EPHE, Montpellier, France
| | - Ndey Bassin Jobe
- Center for Evolution and Medicine, School of Life Sciences, Arizona State University, Life Sciences C, Tempe, United States
| | - Krijn Petrus Paaijmans
- Center for Evolution and Medicine, School of Life Sciences, Arizona State University, Life Sciences C, Tempe, United States
- The Biodesign Center for Immunotherapy, Vaccines and Virotherapy, Arizona State University, Biodesign Institute, Tempe, United States
- ISGlobal, Carrer del Rosselló, Barcelona, Spain
- Centro de Investigação em Saúde de Manhiça (CISM), Distrito da Manhiça, Mozambique
| | - Silvie Huijben
- Center for Evolution and Medicine, School of Life Sciences, Arizona State University, Life Sciences C, Tempe, United States
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Mohammed-Awel J, Iboi EA, Gumel AB. Insecticide resistance and malaria control: A genetics-epidemiology modeling approach. Math Biosci 2020; 325:108368. [PMID: 32437715 DOI: 10.1016/j.mbs.2020.108368] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2020] [Revised: 04/19/2020] [Accepted: 04/29/2020] [Indexed: 11/25/2022]
Abstract
Malaria, a deadly infectious disease caused by the protozoan Plasmodium, remains a major public health menace affecting at least half the human race. Although the large-scale usage of insecticides-based control measures, notably long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS), have led to a dramatic reduction of the burden of this global scourge between the period 2000 to 2015, the fact that the malaria vector (adult female Anopheles mosquito) has become resistant to all currently-available insecticides potentially makes the current laudable global effort to eradicate malaria by 2040 more challenging. This study presents a novel mathematical model, which couples malaria epidemiology with mosquito population genetics, for assessing the impact of insecticides resistance on malaria epidemiology. Numerical simulations of the model, using data relevant to malaria transmission dynamics in the Jimma Zone of Southwestern Ethiopia, show that the implementation of a control strategy based on using LLINs alone can lead to the effective control of malaria, while also effectively managing insecticide resistance, if the LLINs coverage in the community is high enough (over 90%). It is further shown that combining LLINs with IRS (both at reduced and realistically-attainable coverage levels) can lead to the aforementioned effective control of malaria and effective management of insecticide resistance if their coverage levels lie within a certain effective control window in the LLINs-IRS coverage parameter space (this result generally holds regardless of whether or not larviciding is implemented in the community). The study identifies three key parameters of the model that negatively affect the size of the effective control window, namely parameters related with the coverage level of larviciding, the number of new adult mosquitoes that are females and the initial size of the frequency of resistant allele in the community. For the coverage of LLINs and IRS within the effective control window, an additional increase in the values of the aforementioned three parameters may lead to a shrinkage in the size of the effective control window (thereby causing the failure of the insecticides-based control).
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Affiliation(s)
- Jemal Mohammed-Awel
- Department of Mathematics, Valdosta State University, Valdosta, GA 31698, USA.
| | - Enahoro A Iboi
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA
| | - Abba B Gumel
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA
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