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Howerton E, Dahlin K, Edholm CJ, Fox L, Reynolds M, Hollingsworth B, Lytle G, Walker M, Blackwood J, Lenhart S. The effect of governance structures on optimal control of two-patch epidemic models. J Math Biol 2023; 87:74. [PMID: 37861753 PMCID: PMC10589198 DOI: 10.1007/s00285-023-02001-8] [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: 09/09/2022] [Revised: 09/07/2023] [Accepted: 09/14/2023] [Indexed: 10/21/2023]
Abstract
Infectious diseases continue to pose a significant threat to the health of humans globally. While the spread of pathogens transcends geographical boundaries, the management of infectious diseases typically occurs within distinct spatial units, determined by geopolitical boundaries. The allocation of management resources within and across regions (the "governance structure") can affect epidemiological outcomes considerably, and policy-makers are often confronted with a choice between applying control measures uniformly or differentially across regions. Here, we investigate the extent to which uniform and non-uniform governance structures affect the costs of an infectious disease outbreak in two-patch systems using an optimal control framework. A uniform policy implements control measures with the same time varying rate functions across both patches, while these measures are allowed to differ between the patches in a non-uniform policy. We compare results from two systems of differential equations representing transmission of cholera and Ebola, respectively, to understand the interplay between transmission mode, governance structure and the optimal control of outbreaks. In our case studies, the governance structure has a meaningful impact on the allocation of resources and burden of cases, although the difference in total costs is minimal. Understanding how governance structure affects both the optimal control functions and epidemiological outcomes is crucial for the effective management of infectious diseases going forward.
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Affiliation(s)
- Emily Howerton
- Department of Biology and Center for Infectious Disease Dynamics, Pennsylvania State University, University Park, PA, USA
| | - Kyle Dahlin
- Center for the Ecology of Infectious Diseases, Odum School of Ecology, University of Georgia, Athens, GA, USA.
| | | | - Lindsey Fox
- Mathematics Discipline, Eckerd College, Saint Petersburg, FL, USA
| | - Margaret Reynolds
- Department of Mathematical Sciences, United States Military Academy, West Point, NY, USA
| | | | - George Lytle
- Department of Biology, Chemistry, Mathematics, and Computer Science, University of Montevallo, Montevallo, AL, USA
| | - Melody Walker
- Department of Medicine, University of Florida, Gainesville, FL, USA
| | - Julie Blackwood
- Department of Mathematics and Statistics, Williams College, Williamstown, MA, USA
| | - Suzanne Lenhart
- Department of Mathematics, University of Tennessee, Knoxville, TN, USA
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OUEMBA TASSÉ AJ, TSANOU B, LUBUMA J, WOUKENG JEANLOUIS, SIGNING FRANCIS. EBOLA VIRUS DISEASE DYNAMICS WITH SOME PREVENTIVE MEASURES: A CASE STUDY OF THE 2018–2020 KIVU OUTBREAK. J BIOL SYST 2022. [DOI: 10.1142/s0218339022500048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
To fight against Ebola virus disease, several measures have been adopted. Among them, isolation, safe burial and vaccination occupy a prominent place. In this paper, we present a model which takes into account these three control strategies as well as the indirect transmission through a polluted environment. The asymptotic behavior of our model is achieved. Namely, we determine a threshold value [Formula: see text] of the control reproduction number [Formula: see text], below which the disease is eliminated in the long run. Whenever the value of [Formula: see text] ranges from [Formula: see text] and 1, we prove the existence of a backward bifurcation phenomenon, which corresponds to the case, where a locally asymptotically stable positive equilibrium co-exists with the disease-free equilibrium, which is also locally asymptotically stable. The existence of this bifurcation complicates the control of Ebola, since the requirement of [Formula: see text] below one, although necessary, is no longer sufficient for the elimination of Ebola, more efforts need to be deployed. When the value of [Formula: see text] is greater than one, we prove the existence of a unique endemic equilibrium, locally asymptotically stable. That is the disease may persist and become endemic. Numerically, we fit our model to the reported data for the 2018–2020 Kivu Ebola outbreak which occurred in Democratic Republic of Congo. Through the sensitivity analysis of the control reproduction number, we prove that the transmission rates of infected alive who are outside hospital are the most influential parameters. Numerically, we explore the usefulness of isolation, safe burial combined with vaccination and investigate the importance to combine the latter control strategies to the educational campaigns or/and case finding.
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Affiliation(s)
- A. J. OUEMBA TASSÉ
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
| | - B. TSANOU
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
- Department of Science, Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Pretoria 0028, South Africa
- IRD Sorbonne University, UMMISCO, F-93143, Bondy, France
| | - J. LUBUMA
- School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
| | - JEAN LOUIS WOUKENG
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
| | - FRANCIS SIGNING
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
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Wells CR, Pandey A, Parpia AS, Fitzpatrick MC, Meyers LA, Singer BH, Galvani AP. Ebola vaccination in the Democratic Republic of the Congo. Proc Natl Acad Sci U S A 2019; 116:10178-10183. [PMID: 31036657 PMCID: PMC6525480 DOI: 10.1073/pnas.1817329116] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Following the April 2018 reemergence of Ebola in a rural region of the Democratic Republic of the Congo (DRC), the virus spread to an urban center by early May. Within 2 wk of the first case confirmation, a vaccination campaign was initiated in which 3,017 doses were administered to contacts of cases and frontline healthcare workers. To evaluate the spatial dynamics of Ebola transmission and quantify the impact of vaccination, we developed a geographically explicit model that incorporates high-resolution data on poverty and population density. We found that while Ebola risk was concentrated around sites initially reporting infections, longer-range dissemination also posed a risk to areas with high population density and poverty. We estimate that the vaccination program contracted the geographical area at risk for Ebola by up to 70.4% and reduced the level of risk within that region by up to 70.1%. The early implementation of vaccination was critical. A delay of even 1 wk would have reduced these effects to 33.3 and 44.8%, respectively. These results underscore the importance of the rapid deployment of Ebola vaccines during emerging outbreaks to containing transmission and preventing global spread. The spatiotemporal framework developed here provides a tool for identifying high-risk regions, in which surveillance can be intensified and preemptive control can be implemented during future outbreaks.
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Affiliation(s)
- Chad R Wells
- Center for Infectious Disease Modeling and Analysis, Yale School of Public Health, New Haven, CT 06520
| | - Abhishek Pandey
- Center for Infectious Disease Modeling and Analysis, Yale School of Public Health, New Haven, CT 06520
| | - Alyssa S Parpia
- Center for Infectious Disease Modeling and Analysis, Yale School of Public Health, New Haven, CT 06520
| | - Meagan C Fitzpatrick
- Center for Infectious Disease Modeling and Analysis, Yale School of Public Health, New Haven, CT 06520
- Center for Vaccine Development and Global Health, University of Maryland School of Medicine, Baltimore, MD 21201
| | - Lauren A Meyers
- Department of Integrative Biology, University of Texas, Austin TX, 78712
| | - Burton H Singer
- Emerging Pathogens Institute, University of Florida, Gainesville, FL 32610
| | - Alison P Galvani
- Center for Infectious Disease Modeling and Analysis, Yale School of Public Health, New Haven, CT 06520
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Dellicour S, Baele G, Dudas G, Faria NR, Pybus OG, Suchard MA, Rambaut A, Lemey P. Phylodynamic assessment of intervention strategies for the West African Ebola virus outbreak. Nat Commun 2018; 9:2222. [PMID: 29884821 PMCID: PMC5993714 DOI: 10.1038/s41467-018-03763-2] [Citation(s) in RCA: 51] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2017] [Accepted: 03/12/2018] [Indexed: 01/25/2023] Open
Abstract
Genetic analyses have provided important insights into Ebola virus spread during the recent West African outbreak, but their implications for specific intervention scenarios remain unclear. Here, we address this issue using a collection of phylodynamic approaches. We show that long-distance dispersal events were not crucial for epidemic expansion and that preventing viral lineage movement to any given administrative area would, in most cases, have had little impact. However, major urban areas were critical in attracting and disseminating the virus: preventing viral lineage movement to all three capitals simultaneously would have contained epidemic size to one-third. We also show that announcements of border closures were followed by a significant but transient effect on international virus dispersal. By quantifying the hypothetical impact of different intervention strategies, as well as the impact of barriers on dispersal frequency, our study illustrates how phylodynamic analyses can help to address specific epidemiological and outbreak control questions. During the last Ebola virus outbreak in West Africa, a large amount of viral genomic data was obtained. Here, Dellicour et al. use phylodynamic approaches to assess effect of intervention strategies such as border closures.
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Affiliation(s)
- Simon Dellicour
- Department of Microbiology and Immunology, Rega Institute, KU Leuven - University of Leuven, Herestraat 49, 3000, Leuven, Belgium.
| | - Guy Baele
- Department of Microbiology and Immunology, Rega Institute, KU Leuven - University of Leuven, Herestraat 49, 3000, Leuven, Belgium
| | - Gytis Dudas
- Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N, 98109, Seattle, WA, USA
| | - Nuno R Faria
- Department of Zoology, University of Oxford, Oxford, OX1 3PS, United Kingdom
| | - Oliver G Pybus
- Department of Zoology, University of Oxford, Oxford, OX1 3PS, United Kingdom
| | - Marc A Suchard
- Department of Biostatistics, UCLA Fielding School of Public Health, University of California, Los Angeles, CA, 90095, USA.,Department of Biomathematics, David Geffen School of Medicine at UCLA, University of California, Los Angeles, CA, 90095, USA.,Department of Human Genetics, David Geffen School of Medicine at UCLA, University of California, Los Angeles, CA, 90095, USA
| | - Andrew Rambaut
- Institute of Evolutionary Biology, University of Edinburgh, King's Buildings, Edinburgh, EH9 3FL, UK.,Fogarty International Center, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Philippe Lemey
- Department of Microbiology and Immunology, Rega Institute, KU Leuven - University of Leuven, Herestraat 49, 3000, Leuven, Belgium
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