Tree-Grass interactions dynamics and Pulse Fires: mathematical and numerical studies

Savannas are dynamical systems where grasses and trees can either dominate or coexist. Fires are known to be central in the functioning of the savanna biome though their characteristics are expected to vary along the rainfall gradients as observed in Sub-Saharan Africa. In this paper, we model the tree-grass dynamics using impulsive differential equations that consider fires as discrete events. This framework allows us to carry out a comprehensive qualitative mathematical analysis that revealed more diverse possible outcomes than the analogous continuous model. We investigated local and global properties of the equilibria and show that various states exist for the physiognomy of vegetation. Though several abrupt shifts between vegetation states appeared determined by fire periodicity, we showed that direct shading of grasses by trees is also an influential process embodied in the model by a competition parameter leading to bifurcations. Relying on a suitable nonstandard finite difference scheme, we carried out numerical simulations in reference to three main climatic zones as observable in Central Africa.Comment: 51 pages, 7 figure

Parameter Estimation and Optimal Control of the Dynamics Of Transmission of Tuberculosis with Application to Cameroon

This paper deals with the problem of parameter estimation and optimal control of a tuberculosis (TB) model with seasonal fluctuations. We first present a uncontrolled TB model with seasonal fluctuations. We present the theoretical analysis of the uncontrolled TB model without seasonal fluctuations. After, we propose a numerical study to estimate the unknown parameters of the TB model with seasonal fluctuations according to demographic and epidemiological data from Cameroon. Simulation results are in good accordance with the seasonal variation of the new active reported cases of TB in Cameroon. Using this TB model with seasonality, the tuberculosis control is formulated and solved as an optimal control problem, indicating how control terms on the chemoprophylaxis and treatment should be introduced in the considered TB model to reduce the number of individuals with active TB. Results provide a framework for designing cost-effective strategies for TB with two strategies of intervention

Assessing the impact of the environmental contamination on the transmission of Ebola virus disease (EVD)

Please read abstract in the article.The first (T.B.) and the third (J.L.) authors are grateful to the South African Research Chairs Initiative (SARChI Chair), in Mathematical Models and Methods in Bioengineering and Biosciences. The first (T.B.) and the second (S.B.) authors acknowledge the support of Center of Excellence Cameroon (CETIC).https://link.springer.com/journal/121902018-10-01hj2018Mathematics and Applied Mathematic

Modélisation et simulation multi-agent de la propagation d'une épidémie de choléra: cas de la ville de Ngaoundéré

Dans ce travail nous avons utilisé le concept de la modélisation et de la simulation multi-agent pour développer un simulateur qui décrit la dynamique d'une épidémie de choléra. Nous l'avons développé dans la plate-forme multi-agent GAMA 1 en y intégrant le système d'information géographique de la ville de Ngaoundéré comme environnement des agents. Ensuite quelques simulations y ont été exécutées sur un ensemble de jeux de données relatif à la sensibilisation et l'assainissement. Les résultats obtenus à l'issu de ces simulations nous donne de suggérer une stratégie de contrôle optimal axées sur trois points essentiels portant sur l'identification rapide des infectés, la sensibilisation immédiate des populations et surtout de la basse classe et l'assainissement rapide des zones à risque. ABSTRACT. In this work we used the concept of multi-agent modelisation and simulation to conceive one multi-agent model who describe dynamic of cholera epidemic. we implement this model in the multi-agent plate-form GAMA by making use geographical information system of Ngaoundere town as environment. The results obtained suggest an optimal control strategy focused on three essential points relating to the rapid identification of the infected, the immediate awareness of the populations and especially poor people and the rapid sanitation of risk areas

Global stability of a two-patch cholera model with fast and slow transmissions

Please read abstract in the article.The Abdus Salam International Center for Theoretical Physics (ICTP) in Trieste-Italy under the Associateship Scheme, the African Center of Excellence in Information and Communication Technologies (CETIC) in Cameroon and the South African Research Chairs Initiative (SARChI Chair), in Mathematical Models and Methods in Bioengineering and Biosciences.http://www.elsevier.com/locate/matcomhj2021Mathematics and Applied Mathematic

Modélisation et simulation multi-agent de la propagation d'une épidémie de choléra: cas de la ville de Ngaoundéré

In this work we used the concept of multi-agent modelisation and simulation to conceive one multi-agent model who describe dynamic of cholera epidemic. we implement this model in the multi-agent plate-form GAMA by making use geographical information system of Ngaoundere town as environment. The results obtained suggest an optimal control strategy focused on three essential points relating to the rapid identification of the infected, the immediate awareness of the populations and especially poor people and the rapid sanitation of risk areas.Dans ce travail nous avons utilisé le concept de la modélisation et de la simulation multi-agent pour développer un simulateur qui décrit la dynamique d'une épidémie de choléra. Nous l'avons développé dans la plate-forme multi-agent GAMA 1 en y intégrant le système d'information géographique de la ville de Ngaoundéré comme environnement des agents. Ensuite quelques simulations y ont été exécutées sur un ensemble de jeux de données relatif à la sensibilisation et l'assainissement. Les résultats obtenus à l'issu de ces simulations nous donne de suggérer une stratégie de contrôle optimal axées sur trois points essentiels portant sur l'identification rapide des infectés, la sensibilisation immédiate des populations et surtout de la basse classe et l'assainissement rapide des zones à risque

Coupling the modeling of phage-bacteria interaction and cholera epidemiological model with and without optimal control

Please read abstract in the article.The University of Pretoria Senior Postdoctoral Program Granthttp://www.elsevier.com/locate/yjtbihj2021Mathematics and Applied Mathematic