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Cai L, Li X, Tuncer N, Martcheva M, Lashari AA. Optimal control of a malaria model with asymptomatic class and superinfection. Math Biosci 2017; 288:94-108. [PMID: 28284964 DOI: 10.1016/j.mbs.2017.03.003] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2016] [Revised: 02/22/2017] [Accepted: 03/01/2017] [Indexed: 10/20/2022]
Abstract
In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class. If successfully treated, the symptomatic individuals recover and move to the susceptible class. The basic reproduction number, R0, is computed using the next generation approach. The system has a disease-free equilibrium (DFE) which is locally asymptomatically stable when R0<1, and may have up to four endemic equilibria. The model exhibits backward bifurcation generated by two mechanisms; standard incidence and superinfection. If the model does not allow for superinfection or deaths due to the disease, then DFE is globally stable which suggests that backward bifurcation is no longer possible. Simulations suggest that total prevalence of malaria is the highest if all individuals show symptoms upon infection, but then undergoes an incomplete treatment and the lowest when all the individuals first move to the symptomatic class then treated successfully. Total prevalence is average if more individuals upon infection move to the asymptomatic class. We study optimal control strategies applied to bed-net use and treatment as main tools for reducing the total number of symptomatic and asymptomatic individuals. Simulations suggest that the optimal control strategies are very dynamic. Although they always lead to decrease in the symptomatic infectious individuals, they may lead to increase in the number of asymptomatic infectious individuals. This last scenario occurs if a large portion of newly infected individuals move to the symptomatic class but many of them do not complete treatment or if they all complete treatment but the superinfection rate of asymptomatic individuals is average.
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Affiliation(s)
- Liming Cai
- College of Mathematics and Statistic Science, Xinyang Normal University, Xinyang, 46400, CHINA.
| | - Xuezhi Li
- College of Mathematics and information Science, Xinyang Normal University, Xinyang, 46400, CHINA
| | - Necibe Tuncer
- Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA.
| | - Maia Martcheva
- Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105, United States.
| | - Abid Ali Lashari
- Department of Mathematics, Stockholms University, SE-106 91 Stockholm, Sweden
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Maeder MN, Rabezanahary HM, Zafindraibe NJ, Randriatiana MR, Rasamoelina T, Rakotoarivo AT, Vanhems P, Hoffmann J, Bénet T, Rakoto Andrianarivelo M, Rakoto-Alson OA. Sickle-cell disease in febrile children living in a rural village of Madagascar and association with malaria and respiratory infections. BMC HEMATOLOGY 2016; 16:30. [PMID: 27980789 PMCID: PMC5134128 DOI: 10.1186/s12878-016-0069-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2016] [Accepted: 11/17/2016] [Indexed: 11/24/2022]
Abstract
Background In Madagascar, the last study on sickle cell disease (SCD) was done in the early 1980s. The country is known as endemic for malaria and respiratory infections. The main objective of this study was to estimate the prevalence of SCD; the secondary objective was to evaluate its association with malaria and respiratory infections. Methods This is a cross-sectional study which was carried out in a rural village in the south east coast of Madagascar between May 2011 and November 2013. Participants were children aged between 2–59 months presenting with fever measured by axillary temperature ≥37.5 °C at inclusion. Genotyping of haemoglobin S was done by PCR and malaria was diagnosed by Rapid Diagnostic Test. Research for viral and atypical bacterial respiratory pathogens was performed on nasopharyngeal swabs. Uni-and multivariate polytomous logistic regression was done to assess associations between microbiological results and SCD status, with HbAA phenotype as reference. Results A total of 807 children were analysed. Prevalence of SCD among febrile children was 2.4% (95% CI, 1.5–3.7%) and that of SCT was 23.8% (95% CI, 20.9–26.9%). There was no difference in the prevalence of malaria infection according to haemoglobin status (p = 0.3). Rhinovirus (22.5%), adenovirus (14.1%), and bocavirus (11.6%) were the most common respiratory pathogens detected. After univariate analysis, patients with SCD were more frequently infected by parechovirus (p = 0.01), while patients with SCT were more prone to RSV A or B infection (p = 0.01). After multivariate analysis, HbAS phenotype was associated with higher risk of RSV A and B infection compared to HbAA (adjusted OR = 1.9; 95% CI: 1.2–3.1, p = 0.009), while HbSS phenotype was associated with higher risk of parechovirus infection (adjusted OR = 6.0; 95% CI: 1.1–31.3, p = 0.03) compared to HbAA, independently of age, gender, period per quarter, and the other viruses. Conclusion The prevalence of SCD among under-five children presenting with fever was high in the study population. No association was found between SCT and malaria but few viruses, especially parechovirus, seem to play an important role in the occurrence of pneumoniae among SCD patients.
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Affiliation(s)
- Muriel N Maeder
- Centre d'Infectiologie Charles Mérieux, Université Antananarivo, P.O. Box 4299, Antananarivo, Madagascar
| | - Henintsoa M Rabezanahary
- Centre d'Infectiologie Charles Mérieux, Université Antananarivo, P.O. Box 4299, Antananarivo, Madagascar
| | - Norosoa J Zafindraibe
- Centre d'Infectiologie Charles Mérieux, Université Antananarivo, P.O. Box 4299, Antananarivo, Madagascar
| | | | - Tahinamandranto Rasamoelina
- Centre d'Infectiologie Charles Mérieux, Université Antananarivo, P.O. Box 4299, Antananarivo, Madagascar ; UPFR Biochimie-Centre Hospitalier Universitaire Joseph Ravoahangy Andrianavalona, Antananarivo, Madagascar
| | - Andry T Rakotoarivo
- UPFR Biochimie-Centre Hospitalier Universitaire Joseph Ravoahangy Andrianavalona, Antananarivo, Madagascar
| | - Philippe Vanhems
- Laboratoire des Pathogènes Emergents, Fondation Mérieux, Centre International de Recherche en Infectiologie (CIRI), Inserm U1111, CNRS UMR5308, ENS de Lyon, UCBL1 Lyon, France ; Service d'Hygiène, Epidémiologie et Prévention, Hôpital Edouard Herriot, Hospices Civils de Lyon, Lyon, France
| | - Jonathan Hoffmann
- Laboratoire des Pathogènes Emergents, Fondation Mérieux, Centre International de Recherche en Infectiologie (CIRI), Inserm U1111, CNRS UMR5308, ENS de Lyon, UCBL1 Lyon, France
| | - Thomas Bénet
- Laboratoire des Pathogènes Emergents, Fondation Mérieux, Centre International de Recherche en Infectiologie (CIRI), Inserm U1111, CNRS UMR5308, ENS de Lyon, UCBL1 Lyon, France ; Service d'Hygiène, Epidémiologie et Prévention, Hôpital Edouard Herriot, Hospices Civils de Lyon, Lyon, France
| | - Mala Rakoto Andrianarivelo
- Centre d'Infectiologie Charles Mérieux, Université Antananarivo, P.O. Box 4299, Antananarivo, Madagascar
| | - Olivat A Rakoto-Alson
- UPFR Hématologie-Centre Hospitalier Universitaire Joseph Ravoahangy Andrianavalona & Département de Microbiologie, Faculté de Médecine, Antananarivo, Madagascar
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Etoka-Beka MK, Ntoumi F, Kombo M, Deibert J, Poulain P, Vouvoungui C, Kobawila SC, Koukouikila-Koussounda F. Plasmodium falciparum infection in febrile Congolese children: prevalence of clinical malaria 10 years after introduction of artemisinin-combination therapies. Trop Med Int Health 2016; 21:1496-1503. [PMID: 27671736 DOI: 10.1111/tmi.12786] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
OBJECTIVES To investigate the proportion of malaria infection in febrile children consulting a paediatric hospital in Brazzaville, to determine the prevalence of submicroscopic malaria infection, to characterise Plasmodium falciparum infection and compare the prevalence of uncomplicated P. falciparum malaria according to haemoglobin profiles. METHODS Blood samples were collected from children aged <10 years with an axillary temperature ≥37.5 °C consulting the paediatric ward of Marien Ngouabi Hospital in Brazzaville. Parasite density was determined and all samples were screened for P. falciparum by nested polymerase chain reaction (PCR) using the P. falciparum msp-2 marker to detect submicroscopic infections and characterise P. falciparum infection. Sickle cell trait was screened by PCR. RESULTS A total of 229 children with fever were recruited, of whom 10% were diagnosed with uncomplicated malaria and 21% with submicroscopic infection. The mean parasite density in children with uncomplicated malaria was 42 824 parasites/μl of blood. The multiplicity of infection (MOI) was 1.59 in children with uncomplicated malaria and 1.69 in children with submicroscopic infection. The mean haemoglobin level was 10.1 ± 1.7 for children with uncomplicated malaria and 12.0 ± 8.6 for children with submicroscopic infection. About 13% of the children harboured the sickle cell trait (HbAS); the rest had normal haemoglobin (HbAA). No difference in prevalence of uncomplicated malaria and submicroscopic infection, parasite density, haemoglobin level, MOI and P. falciparum genetic diversity was observed according to haemoglobin type. CONCLUSION The low prevalence of uncomplicated malaria in febrile Congolese children indicates the necessity to investigate carefully other causes of fever.
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Affiliation(s)
- Mandingha Kosso Etoka-Beka
- Fondation Congolaise pour la Recherche Médicale, Faculté des Sciences de la Santé, Marien Ngouabi University, Brazzaville, Congo.,Faculté des Sciences et Techniques, Marien Ngouabi University, Brazzaville, Congo
| | - Francine Ntoumi
- Fondation Congolaise pour la Recherche Médicale, Faculté des Sciences de la Santé, Marien Ngouabi University, Brazzaville, Congo.,Faculté des Sciences et Techniques, Marien Ngouabi University, Brazzaville, Congo.,Institute for Tropical Medicine, University of Tübingen, Tübingen, Germany
| | - Michael Kombo
- Fondation Congolaise pour la Recherche Médicale, Faculté des Sciences de la Santé, Marien Ngouabi University, Brazzaville, Congo
| | - Julia Deibert
- Institute for Tropical Medicine, University of Tübingen, Tübingen, Germany
| | - Pierre Poulain
- Fondation Congolaise pour la Recherche Médicale, Faculté des Sciences de la Santé, Marien Ngouabi University, Brazzaville, Congo.,Institut National de la Santé et de la Recherche Médicale U 1134, Paris, France.,UMR_S 1134, DSIMB, Sorbonne Paris Cité, Université Paris Diderot, Paris, France.,Institut National de la Transfusion Sanguine, DSIMB, Paris, France.,UMR_S 1134, Laboratory of Excellence GR-Ex, DSIMB, Paris, France
| | - Christevy Vouvoungui
- Fondation Congolaise pour la Recherche Médicale, Faculté des Sciences de la Santé, Marien Ngouabi University, Brazzaville, Congo
| | | | - Felix Koukouikila-Koussounda
- Fondation Congolaise pour la Recherche Médicale, Faculté des Sciences de la Santé, Marien Ngouabi University, Brazzaville, Congo.,Faculté des Sciences et Techniques, Marien Ngouabi University, Brazzaville, Congo
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Abstract
Sickle cell disease (SCD) is a genetic disorder that poses a serious health threat in tropical Africa, which the World Health Organization has declared a public health priority. Its persistence in human populations has been attributed to the resistance it provides to Plasmodium falciparum malaria in its heterozygous state, called sickle cell trait (SCT). Because of migration, SCT is becoming common outside tropical countries: It is now the most important genetic disorder in France, affecting one birth for every 2,400, and one of the most common in the United States. We assess the strength of the association between SCT and malaria, using current data for both SCT and malaria infections. A total of 3,959 blood samples from 195 villages distributed over the entire Republic of Gabon were analyzed. Hemoglobin variants were identified by using HPLCy (HPLC). Infections by three species of Plasmodium were detected by PCR followed by sequencing of a 201-bp fragment of cytochrome b. An increase of 10% in P. falciparum malaria prevalence is associated with an increase by 4.3% of SCT carriers. An increase of 10 y of age is associated with an increase by 5.5% of SCT carriers. Sex is not associated with SCT. These strong associations show that malaria remains a selective factor in current human populations, despite the progress of medicine and the actions undertaken to fight this disease. Our results provide evidence that evolution is still present in humans, although this is sometimes questioned by scientific, political, or religious personalities.
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Chowell G, Feng Z, Song B. From the guest editors. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2013; 10:i-xxiv. [PMID: 24245643 DOI: 10.3934/mbe.2013.10.5i] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Carlos Castilo-Chavez is a Regents Professor, a Joaquin Bustoz Jr. Professor of Mathematical Biology, and a Distinguished Sustainability Scientist at Arizona State University. His research program is at the interface of the mathematical and natural and social sciences with emphasis on (i) the role of dynamic social landscapes on disease dispersal; (ii) the role of environmental and social structures on the dynamics of addiction and disease evolution, and (iii) Dynamics of complex systems at the interphase of ecology, epidemiology and the social sciences. Castillo-Chavez has co-authored over two hundred publications (see goggle scholar citations) that include journal articles and edited research volumes. Specifically, he co-authored a textbook in Mathematical Biology in 2001 (second edition in 2012); a volume (with Harvey Thomas Banks) on the use of mathematical models in homeland security published in SIAM's Frontiers in Applied Mathematics Series (2003); and co-edited volumes in the Series Contemporary Mathematics entitled '' Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges'' (American Mathematical Society, 2006) and Mathematical and Statistical Estimation Approaches in Epidemiology (Springer-Verlag, 2009) highlighting his interests in the applications of mathematics in emerging and re-emerging diseases. Castillo-Chavez is a member of the Santa Fe Institute's external faculty, adjunct professor at Cornell University, and contributor, as a member of the Steering Committee of the '' Committee for the Review of the Evaluation Data on the Effectiveness of NSF-Supported and Commercially Generated Mathematics Curriculum Materials,'' to a 2004 NRC report. The CBMS workshop '' Mathematical Epidemiology with Applications'' lectures delivered by C. Castillo-Chavez and F. Brauer in 2011 have been published by SIAM in 2013.
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Affiliation(s)
- Gerardo Chowell
- Mathematical, Computational and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Box 872402, Tempe, AZ 85287, United States.
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