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Derdei Mahamat Bichara Ph.D.

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Derdei Mahamat Bichara Ph.D.

Associate Professor
Department of Mathematics

Contact

Email: dbichara@fullerton.edu 
Phone: (657) 278-3196

Office Location

MH-178, McCarthy Hall
800 N State College Blvd
Department of Mathematics
California State University, Fullerton, CA 92831

Derdei Mahamat Bichara

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About Me

Welcome to my homepage! Before we go any further, I want to point out that though Bichara appears to be my last name, it is also my given name. So, I go by Bichara (pronounced as Beeshara). I received my Ph.D. in mathematics from the University of Lorraine, France. I subsequently joined Arizona State University as a postdoc. I am currently an Associate Professor at California State University, Fullerton.

Research Interests:

My broad research interests are dynamical systems, mathematical biology and control theory. I am particularly keen to modeling problems that address relevant biological, ecological or epidemiological questions and analyze them through theoretical analysis and simulations. Most of these models take the form of large system of differential equations. Asymptotic behavior of the solutions of these systems in terms of some thresholds is then investigated in order to gain insight into the overall dynamics of the considered problem.

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Education

  • Ph.D. Mathematics, University of Lorraine, France. (2013)
  • M.S. Applied Mathematics, University of Saint-Louis, Senegal. (2008)
  • B.S. Mathematics of Decision, Cadi Ayyad University, Marrakesh, Morocco. (2005)

Professional Experience

  • Postdoctoral Research Associate, Arizona State University (2013-2016)
  • ATER, University of Lorraine (2011-2012)

Professional Organization Membership

  • American Mathematical Society (A.M.S)
  • Mathematical Association of America (M.A.A)
  • Society for Industrial and Applied Mathematics (S.I.A.M)
  • Society for Mathematical Biology (B.M.B)
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Research

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Summary

My research interests lie at the crossroads of dynamical systems, mathematical modeling, and computational sciences. A common thread in my research is exploring problems that arise in population dynamics, control theory, and epidemiology by using tools of applied analysis and computational methods to characterize these models in order to address relevant biological or epidemiological questions.

Overview

Typically, my research is structured into two key components. The first step is to better understand these biosystems in order to formulate mathematical models that describe these phenomena. Oftentimes, these models are represented by nonlinear dynamical systems. The second step is to mathematically analyze these problems to gain insights and characterize the initial problems. These two undertakings are synergetic: biological questions lead to new challenges in mathematics, and the study of these mathematical problems provide tools in understanding the behavior of natural phenomena. My focus is on three primary areas of research detailed below. But before weaving into details, a word cloud of my research is this image (shout-out to those who recognized the shape of the cloud).

Word Cloud

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  1. Residence times concepts and Lagrangian approaches: I have developed a new framework in modeling infectious diseases which consists of using environmental risk factors and proportion of times spent in these environment – or patches – as a proxy of contact rates, which are difficult to measure or define for communicable diseases. These investigations have led to advances in understanding the effects of virtual dispersal,  heterogeneity in groups and patches among others.
  2. Residence times concepts and Lagrangian approaches: I have developed a new framework in modeling infectious diseases which consists of using environmental risk factors and proportion of times spent in these environment – or patches – as a proxy of contact rates, which are difficult to measure or define for communicable diseases. These investigations have led to advances in understanding the effects of virtual dispersal, heterogeneity in groups and patches among others.
  3. States and parameters estimation: The estimation of unknown parameters and some state variables is a notorious problem in epidemiology. Indeed, in many epidemic models, the transmission parameter, the index cases (as a component of the initial conditions of the dynamical system), the number of latent, or the total number of mosquito populations are not known. I have developed methods to estimate parameters and state variables for some epidemic models using tools of control theory.
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Publications and Projects

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Projects

I am looking for undergraduate students interested in research experiences. A grade of B or above in a differential equations course (MATH 250B, Math 340 or MATH 310) is required. Contact me for more information.

 

Publications

  1. P. Adda and D. M. Bichara: Global Stability of SIR and SIRS models with differential mortality, Inter. Jour. of Pure and Applied Mathematics, Vol. 80, No 3, pp. 425-433, 2012.
  2. D. M. Bichara: Étude de modèles épidémiologiques: Stabilité, observation et estimation de paramètres, PhD Thesis, University of Lorraine, (2013).
  3. D. M. Bichara, A. Iggidr and G. Sallet: Global analysis of multi-strain SIS, SIR and MSIR epidemic models, Journal of Applied Mathematics and Computing, Vol. 44, pp. 273-292, 2014 [PDF]
  4. H. D Toro Zapata, A. G Caicedo Casso, D. M. Bichara, S. Lee: Role of active and inactive cytotoxic immune response in human immunodeficiency virus dynamics, Osong Public Health and Research Perspectives,5(1):3-8, 2014.
  5. D. M. Bichara, N. Cozic and A. Iggidr: On the estimation of sequestred infected erythrocytes in Plasmodium falciparum patients, Mathematical Biosciences and Engineering, Vol 11, 4, 2014 [PDF]
  6. D. M. Bichara, Y. Kang, C. Castillo-Chavez, R. Horan and C. Perrings: SIS and SIR epidemic models with virtual dispersal and residence times, Bulletin of Mathematical Biology, (2015), 77,  2004 [PDF]
  7. B. Espinoza, V. Moreno, D. M. Bichara and C. Castillo-Chavez: Assessing the Efficiency of Movement Restriction as a Control Strategy of Ebola, In Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, Editors: Gerardo Chowell and James M. Hyman, Springer, 2016 [PDF]
  8. C. Castillo-Chavez, K. Barley, D. M. Bichara, D. Chowell, E. Diaz Herrera, B. Espinoza, V. Moreno, S. Towers and K. E. Yong: Modeling Ebola at the Mathematical and Theoretical Biology Institute (MTBI), Notices of the AMS, Vol. 63, No 4, 2016.
  9. V. M. Moreno, B. Espinoza, D. M. Bichara, S. A. Holechek and C. Castillo-Chavez: Role of short-term dispersal on the dynamics of Zika virus in an extreme idealized environment, Infectious Disease Modelling, (2016) [PDF]
  10. D. M. Bichara, S. A. Holechek, J. Velázquez-Castro, A. L. Murillo and C. Castillo-Chavez: On the dynamics of dengue virus type 2 with residence times and vertical transmission, Letters in Biomathematics, Vol. 3, No. 1, (2016), 140–160 [PDF]
  11. D. M. Bichara and C. Castillo-Chavez: Vector-borne diseases models with residence times - a Lagrangian approach, Mathematical Biosciences, 281, 128–138, 2016 [PDF]
  12. C. Castillo-Chavez, D. Bichara and B. R. Morin: Perspectives on the role of mobility, behavior, and time scales in the spread of diseases, Proc Natl Acad Sci USA, 113 (2016) 4582-14588 [PDF]
  13. D. M. Bichara and A. Iggidr: Multi-Patch and Multi-Group Epidemic Models: A New Framework, Journal of Mathematical Biology, DOI 10.1007/s00285-017-1191-9, 2017 [PDF]
  14. D. M. Bichara, A. Iggidr and L. Smith: Multi-stage Vector-Borne Zoonoses Models: A Global Analysis, Bulletin of Mathematical Biology, DOI 10.1007/s11538-018-0435-1, 2018 [PDF]
  15. D. M. Bichara: Global Analysis of Multi-Host and Multi-Vector Epidemic Models, Journal of Mathematical Analysis and Applications, Vol. 475, No. 2, 2019 [PDF]
  16. D. M. Bichara: Effects of migration on vector-borne diseases with forward and backward stage progression, Discrete and Continuous Dynamical Systems -- Series B, DOI: 10.3934/dcdsb.2019140, 2019 [PDF]
  17. D. M. Bichara, A. Guiro, A. iggidr, D. Ngom: State and Parameter Estimation for a Class of Schistosomiasis Models, Mathematical Biosciences, DOI: 10.1016/j.mbs.2019.108226, 2019 [PDF]

Technical Reports

  1. C. Mohanakumar, A. E. Offer, J. Rodriguez, B. Espinoza, V. Moreno, F. Nazari, D. Bichara, C. Castillo-Garsow: Mathematical Model for Time to Neuron Apoptosis Due to Accrual of DNA DSBs, Mathematical and Theoretical Biology Institute, July, 2015.
  2. J. Burkow, A. Singh, V. Valle, J. Velazquez, D. Padilla, J. Renova, L. Arriola, D. Bichara: A Model for Stripe Rust Growth with Two Fungicidal Effects, Mathematical and Theoretical Biology Institute, July, 2014.
  3. J. Tapia, D. Bichara: Political Recruitment via Television Ads in a Two-Party System, Mathematical and Theoretical Biology Institute, July, 2014.
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