International Conference on Bio-Mathematics (July 1 – 2, 2022)

Speaker: Professor Julien Arino (University of Manitoba, Canada)

Contact: For any questions or comments, please contact one of the organizers

Host :
Prof Mahamat S Daoussa Haggar (Director of the Modeling, Mathematics, Computer Science, Applications and Simulation Laboratory – University of N’Djamena, Chad;

Scientific Committee:
Prof Mohamed Mbehou (University of Yaounde I, cameroon) – Chair
Prof Julien Arino (Manitoba University, Canada)
Prof Florence Hubert (Aix-Marseille University, France)
Prof Legesse Obsu (Adama Science and Technology University, Ethiopia)
Prof Benjamin Mampassi (Cheikh Anta Diop University, Senegal)
Prof Koina Rodoumta (University of N’Djamena, Chad)
Dr Mihaja Ramanantoanina (University of Pretoria, South Africa)

CIMPA (International Center for Pure and Applied Mathematics)
3MC (Mathematical Modeling Mini Courses)

Prof Mahamat Saleh Daoussa Haggar (Université de N’Djamena, Tchad)
Prof Bakari Abbo (Université de N’Djamena, Tchad)
Dr Patrick Tchepmo Djomegni (North West University, South Africa)
Dr Yaya Moussa (Université de N’Djamena, Tchad)
Mr Abdramane Annour Saad (Université de N’Djamena, Tchad)
Mrs Kadidja Mahamad Malloum (Université de N’Djamena, Tchad)
Mrs Raouda Amine Oumar (Université de N’Djamena, Tchad)

Theprogram is the following

FRIDAY 01 JULY  2022
08 :50 – 09 :00 Opening by Prof. Mahamat Saleh Daoussa Haggar (President of the University of N’Djamena)
09 :00 – 10 :00 Plenary talk by Prof Julien Arino
10 :05 – 10 :45 Talk 1: Dr Mihaja Ramanantoanina
10 :50 – 11 :30 Talk  2: Prof Mohamed Mbehou
11 :30 – 12 :00 Tea break
12 :00 – 12 :40 Talk 3: Dr Patrick Tchepmo
12 :40 – 14 :10 Lunch
14 :10 – 14 :40 Talk 4: Mr Aminou M Layaka
14 :40 – 15 :10 Talk 5: Mr Annour Saad Abdramane
15 :10 – 15 :40 Talk 6: Mr Dawè Siguy
09 :00 – 10 :00 Plenary talk by Prof Florence Hubert
10 :05 – 10 :45 Talk 7: Dr David Fotsa Mbogne
10 :50 – 11 :30 Talk 8: Dr Komi Afassinou
11 :30 – 12 :00 Tea break
12 :00 – 12 :40 Talk 9: Mr Aminou M Layaka
12 :40 – 14 :10 Lunch
14 :10 – 14 :40 Talk 10: Issa Oumar Abdallah
14 :40 – 15 :10 Talk 11: Guibé Séhoré
15 :10 – 15 :40 Talk 12: Vérité Djimasnodji
15 :40 – 16 :00 Closing by Prof. Mahamat Saleh Daoussa Haggar (President of the University of N’Djamena)

Prof Julien Arino (University of Manitoba, Canada)
Title: Imports of COVID-19 cases
The spatio-temporal spread of COVID-19 was rapid, with most countries around the world reporting cases within months. But if we look more closely, the situation was much more heterogeneous than it appears at first sight. If we consider local jurisdictions, we observe that many of them, in particular those whose population is not very high, experienced alternating phases of active spread of the disease and phases during which the disease was absent. This poses the problem of case imports: under what conditions does a jurisdiction that does not experience local propagation chains at a given time go into the epidemic phase following one or more case imports? I will present a class of models allowing to consider this kind of problems. I will also show how we can assess the contribution of imported cases to the dynamics of local spread, as well as the effectiveness of some measures aimed at reducing the risk of imported cases.

Prof Florence Hubert (Aix-Marseille University, France)
Titre: Les modèles de croissances-fragmentation en oncologie
Fragmentation growth models are commonly used in structured population dynamics to describe, for example, cell division phenomena or polymerization phenomena. The most classical equation is the following

The study of the global existence of solutions to this problem as well as the study of their asymptotic behavior has given rise to many works. We will start by giving the main applications of such a model, then we will recall the main results (see [1], [4]). We will then propose extensions of this model used in oncology to describe the phenomena of metastatic emission or to describe the dynamic instabilities of microtubules. We will review the known results on these models and the remaining challenges.
[1] J. A. Cañizo, P. Gabriel, and H. Yoldas. Spectral gap for the growth-fragmentation equation via Harris’s theorem. SIAM J. Math. Anal., Vol.53, No.5, pp.5185-5214,(2021)
[2] N. Hartung, S. Mollard, D. Barbolosi, A. Benabdallah, G. Chapuisat, G. Henry,S. Giacometti, A. Iliadis, J.Ciccolini, C. Faivre, F. Hubert. Mathematical Modeling of tumor growth and metastatics spreading : validation in tumor-bearing mice, Cancer Research 74, p. 6397-6407, 2014.
[3] S. Honoré, F. Hubert, M. Tournus, D. White. A growth-fragmentation approach for modeling microtubule dynamic instability, Bulletin of Mathematical Biology, 81 p. 722–758 (2019)
[4] B. Perthame. Transport equations in biology, Springer.

Prof. Mohamed Mbehou (University of Yaounde I, cameroon)
Title: Numerical implementation of non/local PDEs using finite element methods
This work is devoted to the study of the finite element approximation for non/local nonlinear parabolic problems. The first part will be based on the presentation of some nonlocal and local problems. While the following will be on the implementation of a 1D/ 2D nonlocal PDE via the use of the software Matlab.

Dr Patrick Tchepmo Djomegni (North West University, South Africa)
Titre: Coexistence and harvesting control policy in a food chain model
We present the rich dynamics in two mathematical food chain models. The first case presents harvest regulation strategies in order to preserve the survival of species and optimize profits. The second case presents the effect of response functions on species persistence. Hopf bifurcation, limit cycle, doubling periods, chaotic attractors, border crises are observed in the numerical calculations

Dr Mihaja Ramanantoanina (University of Pretoria, South Africa)
Title: On some spatio-temporal models of mutualistic populations.
In this talk, we review some approaches to model the spatio-temporal dynamics of two species engaged in a mutualistic interaction. First, we address the case of continuously reproducing species using reaction-diffusion models based on partial differential equations. Next, we consider the case of species with non-overlapping generations. In this case, the movement is captured by a dispersion kernel (a probability distribution that an individual moves from one place to another), and the population dynamics are modeled using integro-difference systems . In both cases, we focus on the wavefront profiles and the propagation rate of the populations.

Dr Komi Afassinou (University of Zululand, South Africa)
Title: Mathematical modeling of foodborne disease transmission by cockroaches in human dwellings.
Cockroaches are among the most common pests in many homes and other food processing areas. Their cohabitation with humans has raised public health concerns and poses serious risks to human health, as they are believed to play an important role in the transmission of various intestinal diseases such as diarrhea, dysentery, cholera, leprous plague and typhoid fever. In this article, we present a mathematical model that depicts the transmission of foodborne diseases to humans by cockroaches. We incorporate control interventions such as the use of insecticides and regular environmental sanitation. Mathematical and numerical analyzes are conducted to investigate the impact of these control interventions when considered as single or combined strategies. The results obtained reveal the level of effectiveness of insecticides beyond which total eradication is possible, especially when their use is combined with regular sanitation of the environment. Use of bait and trap devices is also explored and it turns out to be the best strategies.
[2] Ifeanyi O.T., Odunayo O.O., Microbiology of Cockroaches – A Public Health
Concern, International Journal of Scientific Research 4, 4 (2015).
[3] Keiding J., the cockroach-biology and control: Training and information guide
(advanced level), Geneva, World Health Organization, (1986) 86:937.
[4] Aliya H.B., In celebration of cockroaches, Daily Califormia.

Dr David Fotsa Mbogne (Université de Ngaoundéré, Cameroun)
Title: Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon.
This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory coronavirus 2 (SARS-CoV-2). A multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism is proposed first. Indeed, there are human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self-infection by susceptible individuals. The global stability of the disease-free equilibrium is shown when a given threshold T0 is less or equal to 1 and the basic reproduction number R0 is calculated. A convergence index T1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of infectious extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. Using Partial Rank Correlation Coefficient with a three levels fractional experimental design, the sensitivity of R0, T0 and T1 to control parameters is evaluated. Following this study, the most significant parameter is the probability of wearing a mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into account economic impacts of SARS-CoV-2, optimal fighting strategies are determined and discussed. The study is applied to real and available data from Cameroon with a model fitting. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy against SARS-CoV-2.

Dr Djibe Mbainguesse (University of N’Djamena)
Title: Numerical methods for nonlinear heat equation subject to nonlocal boundary conditions
We present a combinaison of three methods to produce an approximate solution of nonlinear heat equation of nonlocal boundary conditions. We first use the implicit backward Euler’s method to reduce the equation to a boundary value problem with x as the spatial variable independent. The finite difference method of order four is then employed together with the Simpson’s quadrature to transform the problem in the form of nonlinear algebric systems. We ressort to Newton’s iteration procedure to obtain the approximate solution.

Aminou M. Layaka (PhD student, L2MIAS, University of N’Djamena, Chad)
Title: Modelling and stability analysis of immune regulatory mechanisms during malaria blood stage infection
Malaria infection gives rise to host response which is regulated by both the immune system as well as by the environmental factors. In this talk, we discuss the immune regulation of malaria blood stage infection in humans, focusing on Plasmodium falciparum, the most widely spread and dangerous of the human malaria parasites. We also propose some differential equations which describe the dynamics of the immune cells and their cytokines interacting against the blood stage malaria parasite. Then we study the stability of the system at the equilibrium point

Aminou M. Layaka (PhD student, L2MIAS, University of N’Djamena, Chad)
Title: Optimal Control Analysis of Intra-Host Dynamics of Malaria with Immune Response

In this talk, a new intra-host model of malaria that describes the dynamics of the blood stages of the parasite and its interaction with red blood cells and immune cells is formulated. The qualitative properties of solutions are established. We then extend the model to incorporate, in addition to immune response, three control variables. The existence result for the optimal control triple, which minimizes malaria infection and costs of implementation, is explicitly proved. Finally, we apply Pontryagin’s Maximum Principle to the model in order to determine the necessary conditions for optimal control of the disease.

Guibé Séhoré (L2MIAS, University of N’Djamena, Chad)
Title: Mathematical model study of two-strain tuberculosis with reinfection
We are studying the dynamics of tuberculosis infection with two strains: the susceptible and resistant to treatment. We consider an S-Es-Is-Er-Ir-T model with reinfection proposed by Castillo Chavez. We study the local and global stability of the equilibrium points, then examine the sensitivity of the reproduction number with respect to certain parameters of the model.

Issa Oumar Abdallah (PhD student, L2MIAS, University of N’Djamena, Chad)
Title: Strategies for optimal control of the dynamics of the Covid-19 virus
In this talk, we introduce two controls in a model describing the infection dynamics of the Covid-19 virus in the body. Optimal control strategies are determined by minimizing infections, viral production and considering treatment and physiological costs. First, we use a result of Fleming and Rishel to establish the existence of the optimal control. Then, we characterize the optimal control and establish its uniqueness. Finally, the numerical simulation allowed us to illustrate our results and to quantify the impact of the control on the dynamics of infection.

Annour Saad Abdramane (PhD student, L2MIAS, University of N’Djamena, Chad)
Title: Mathematical Modeling of COVID-19: Case of Viral Infection with Inflammatory Response
In this work, we analyze a virus model of SARS-CoV-2 infection with immune response. The model was proposed by Mochan et al (2021) and describes an experiment carried out on Macaques. We analyze it analytically for the first time by studying its qualitative behavior. We establish the existence, uniqueness and positivity of the solution. Then we determine the equilibrium points, study their stability, and investigate strategies to limit secondary infections via a sensitivity study. The susceptibility index results indicate reducing the rate of virus replication is the best strategy to reduce secondary infections. The theoretical results are illustrated graphically.

Dawè Siguy (L2MIAS, University of N’Djamena, Chad)
Title: Study and Simulations of Mathematical Models in Neuroscience
In this work, we describe the neuron and its components, present some mathematical models in neurosciences in particular the model of Hodgkin and Huxley and some of its derivatives. We are mainly interested in the Fitzhugh-Nagumo model for which we study the existence and uniqueness of solutions, determine the equilibrium points and their nature, then the existence and direction of Hopf bifurcation. Finally, the numerical model obtained using a finite difference scheme is simulated in Matlab. The study will be limited because of its complexity.
Keywords: Model in neuroscience, FitzHugh-Nagumo, equilibrium point, stability, bifurcation, finite difference method.

Vérité Djimasnodji (PhD student, University of N’Djamena, Chad)
Title: 2-species chemotaxis model with volume filling effect; Prey-predator system with multi-taxis
The presentation focuses on the mathematical and numerical analysis of a 2-species chemotaxis model with volume effect. After the modeling of the phenomenon by using some physical laws, we will make the mathematical analysis of the model then the discretization by the Finite Elements method of the Galerkin type and the semi-implicit Euler scheme. We will present the numerical results obtained following some numerical simulations. Finally, we briefly present prey-predator systems with multi-taxis which is a general case of what is presented above.

Registration for this event are closed

Participants list:

  1. Prof Julien Arino, University of Manitoba, Canada
  2. Prof Florence Hubert, Aix-Marseille University, France
  3. Prof Mahamat Saleh Daoussa Haggar, Université de N’Djamena, Tchad
  4. Prof Legesse Obsu, Adama Science and Technology University, Ethiopie
  5. Prof Mohamed Mbehou, Université de Yaoundé I, cameroun
  6. Dr Komi Afassinou, University of Zululand, South Africa
  7. Dr Mihaja Ramanantoanina, University of Pretoria, South Africa
  8. Dr Patrick Tchepmo Djomegni, North West University, South Africa
  9. Eucharia Nwachukwu, University of Port Harcourt, Nigeria
  10. Junior Kaningini, AIMS-Senegal, Senegal
  11. Camelle Kabiwa Kadje, University of Douala, Cameroon
  12. Bahati Kilongo, AIMS-Senegal, Senegal
  13. Dr David Fotsa-Mbogne, Université de Ngaoundéré, Cameroun
  14. Frais Kwadzo Agbenyegah, Ghana Communication Technology University, Ghana
  15. Dr Lema Logamou Seknewna, AIMS-Senegal, Senegal
  16. Patient Murhula Buhendwa, AIMS-Cameroon, Cameroon
  17. Djokdelang Aloumza, Université de N’Djamena, Chad
  18. Nassouradine Mahamat Hamdan, Université de N’Djamena, TChad
  19. Kalidou Aliou Ball, Université Gaston Berger de Saint Louis, Senegal
  20. Olusanmi Odeyemi, University of Benin, Nigeria
  21. Issa Oumar Abdallah, L2MIAS, Université de N’Djamena, Tchad
  22. Younous Magdoum, FSEA, Tchad
  23. Kevin Basita, Technical University of Kenya, Kenya
  24. Néhémie Néribar Djibé, Tchad
  25. Winnie Yaa, AIMS-Senegal, Senegal
  26. Bienvenu Djonneyahe, L2MIAS, Université de N’Djamena, Tchad
  27. Faustin Koumakoye Makrada, Université de N’Djamena, Tchad
  28. Annour Saad Abdramane, L2MIAS, Université de N’Djamena, Tchad
  29. Oumar Madaï, L2MIAS, Université de N’Djamena, Tchad
  30. Raounda Amine Oumar, L2MIAS, Université de N’Djamena, Tchad
  31. Sehore Guibe, L2MIAS, Université de N’Djamena, Tchad
  32. Djimramadji Hippolyte, L2MIAS, Université de N’Djamena, Tchad
  33. Mopeng Herguey, L2MIAS, Université de N’Djamena, Tchad
  34. Ahmad Ouaman Okari, L2MIAS, Université de N’Djamena, Tchad
  35. Bienvenu Ndonane, L2MIAS, Université de N’Djamena, Tchad
  36. Khadidja Mahamat Malloum, L2MIAS, Université de N’Djamena, Tchad
  37. Djerayom Luc, L2MIAS, Université de N’Djamena, Tchad
  38. Oumar Moussa Godi, L2MIAS, Université de N’Djamena, Tchad
  39. Okari Ahmad, L2MIAS, Université de N’Djamena, Tchad
  40. Dawe Siguy, L2MIAS, Université de N’Djamena, Tchad
  41. Abakar Himeda Abdarahman, Université de N’Djamena, Tchad
  42. Alex Lawou Meli, AIMS-Cameroon, Cameroon
  43. Mahamat Abakar Adoum, Université de N’Djamena, Tchad
  44. Idriss Cabrel Tsewalo Tondji, AIMS-Sénégal, Sénégal
  45. Joseph Romaric Cheuteu Tazopap, Université de Douala, Cameroun
  46. Elkana Koungue Gueini, Tchad
  47. Issa Ahmat Annour, Université Gaston Berger de saint louis, Senegal
  48. Arielle Sonia Yonke Nana, Université de Yaoundé I, Cameroun
  49. Mady Parguet, Université de N’Djamena, Tchad
  50. Merveille Cyndie Talla Makougne, Université de Yaoundé I, Cameroun
  51. Astou Ndima, AIMS-Senegal, Senegal
  52. Oleï Tahar Hassane, L2MIAS, Université de N’Djamena, Tchad
  53. Alphonse Gapili Onsou, Université de Douala, Cameroun
  54. Léonel KEMFOUET TSOPZÉ, Université de Yaoundé 1, Cameroun
  55. Manuela Metsadong Nimpa, Université de Douala, Cameroun
  56. Joseph Romaric Cheuteu Tazopap, Université de Douala, Cameroun 
  57. Sthyve Junior Tatho Djeanou, Université de Douala, Cameroun
  58. Henri Loic Nguejo Messa, Université de Yaoundé 1
  59. Annour Djidda Mahamat, Université de N’Djamena, Tchad
  60. Mahamat Abakar Abdallah, Université de N’Djamena, Tchad
  61. Magloire Ndilnodji, Université de N’Djamena, Tchad 
  62. Vérité Djimasnodji, Université de N’Djamena, Tchad 
  63. Ablaye Ngalaba, Université de N’Djamena, Tchad 
  64. Mahamat Abakar Djalabi, Université de N’Djamena, Tchad
  65. Mahamat Saleh Idriss Ibrahim, Université de N’Djamena, Tchad