Biomathematics

 Dr. Yatat Djeumen ,  email: [email protected], phone: +237 675305726

DESCRIPTION OF BIOMATHEMATICS

At ACAS, the research thematic on Biomathematics deals with works on various topics ranging from Mathematical Biology (vector-borne diseases modelling, vectors/pests controls) to Mathematical Agronomy (banana plant vs pest modelling and control) through Mathematical Ecology (forest-savanna interactions modelling). Precisely, we develop, study and simulate realistic and meaningful mathematical models in order to get new insights.

“Mathematics Is Biology’s Next Microscope, Only Better; Biology Is Mathematics’ Next Physics, Only Better”, J. E. Cohen, 2004.

 

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Members

Torsten Meier

Dr. Yatat Djeumen, ACAS and Lectuer, NASEY

Email : [email protected]

Brief Presentation

I am an applied mathematician working in the field of mathematical modeling in life sciences (biology, ecology). In particular, I focus on mathematical tools/methods/approaches that provide new insights to specific issues arising in Ecology or in Biology.

International award

2016: Ibni Oumar Mahamat Saleh Prize for 2015 as the best young mathematician of Central and West Africa. The Ibni Prize has been created in 2009 by the French Mathematical Societies. The winner is selected after review by a scientific committee appointed by ICPAM (International Center for Pure and Applied Mathematics). www.smf.emath.fr/actualites-smf/proclamation-des-resultats-du-prix-ibni-o-m-saleh-2015

Research Activities

My main research domain is mathematical modeling with applications mainly in Ecology and also in Epidemiology.

In the first branch of my work, which is a continuation of my PhD works, I study tree-grass interactions in savanna ecosystems taking into account disturbances like fire and herbivory.     Understanding the possible long-term distribution of woody and grassy biomass values within the savanna ecosystems of Africa is an important challenge because savannas are home of a very diversified fauna and support of livelihoods for large and growing human populations, while vegetation dynamics and fires are of utmost importance to understand the carbon balance. Hence, we recently submitted a manuscript that deals with the study of a minimalistic space-implicit ODE-based savanna model that renders tree-grass distributions along biogeographic gradient and developed an easy-to-use R-shiny application to let readers easily draw model bifurcation diagrams with respect to parameters of a given ecological context (see Yatat et al. (2021)). In our work we also take into account the discrete nature of fire occurrences. Precisely, in Yatat et al. (2018b), (2017),  we proposed and studied space-implicit IDE-based savanna models where the discrete nature of fires is considered as periodic and impulsive events.   In Yatat et al. (2018a) a space-explicit PDE-based savanna model is studied to discriminate the impact of (impulsive) fire regime on the dynamics of a mosaic of forest and grassland in a context of humid climates in Central Africa where forest-savanna mosaics are frequently observed while forest dominates over most of the area and can be assumed as stable. We discussed and characterized how fires may be able to slow down, stop or even reverse the sign of the bistable forest-grassland travelling wave solution. Specifically, we show that fires may greatly slow down, stop or reverse the progression of forest in humid regions. Acknowledging the discrete nature of fire occurrences, we studied in Banasiak et al. (2019) and in Yatat and Dumont (2018), the existence of travelling wave solutions for impulsive reaction-diffusion equations with an application to fire-prone savannas, to show how impulsive fires may control/limit forest encroachment in humid regions.

In the second part of my postdoctoral works, I am studying the feasibility of the Sterile Insect Technique (SIT) as a control tool of vector/pest population. The aim is to use (mathematical) modeling to improve SIT field protocols, or test assumptions that could be difficult to verify in real conditions. In a recent work, we obtained a threshold number of treated males above which the control of wild population is effective using massive releases, that, in the field, are only possible for a short period. When the amount of treated males is lower than the aforementioned threshold, %the SIT control induces a bistability involving the elimination equilibrium (0) and a positive equilibrium (E_2) are simultaneously stable while another unstable equilibrium (E_1) lies between 0 and E_2. Hence, the “Trapping box" strategy consists of first doing massive releases of treated males to lower the wild population under E_1 and then, use low level and more sustainable releases to maintain the wild population under E_1 and ensuring their long term elimination.

We also estimated, numerically, the minimal time necessary to enter the box [0, E_1) (see Anguelov et al. 2020).

Last two years peer-reviewed articles

  1. Yatat Djeumen, Y. Dumont, A. Doizy, P. Couteron. A minimalistic model of vegetation physiognomies in the savanna biome. Ecological Modelling. Volume 440, 15 January 2021, 109381. https://doi.org/10.1016/j.ecolmodel.2020.109381
  2. Banasiak, Y. Dumont and I. V. Yatat Djeumen. Spreading speeds and traveling waves for monotone systems of impulsive reaction-diffusion equations. Differential Equations and Dynamical Systems, (2020). https://doi.org/10.1007/s12591-020-00552-6

Anguelov R, Dumont Y, I. V. Yatat Djeumen. Sustainable vector/pest control using the permanent sterile insect technique. Math. Meth. Appl. Sci., 1-22, (2020).  www.doi.org/10.1002/mma.6385

Didier Belobo

Dr. Belobo Belobo Didier, ACAS

Email : [email protected]

phone: + 237 673635393

Publications