Optimal control of the treatment frequency in a stochastic model of tuberculosis

This paper presents a stochastic model of the Tuberculosis (TB) infection with treatment in a population composed of four individuals compartments: susceptible individuals, latent infected individuals, active infected individuals and recovered individuals after the therapy. The mathematical model of TB infection includes in addition to the deterministic term, a stochastic term that translates the random noise. The random nature of this model is due to the fact that the contraction of the Mycobacterium Tuberculosis, the vector agent of the TB infection and his transmission within the population are done in a random manner according to the variable efficiency of control of the immune system of the individuals. While supposing that only the active infected individuals transmit the infection, their survey in order to observe the rules of hygiene, to adopt a positive behavior with respect to the susceptible individuals (who must also take some precautions) to follow the treatment up to finish, constitute measures of adequate control.  A preliminary survey of the model is made before approaching the crucial left of the topic.  The main objective of this paper is to control the frequency of treatment in a stochastic model of the TB infection while minimizing the cost of the measures. We formulate an optimal control problem that consists in minimizing the relative cost to the dynamics of the model in order to reduce the prevalence and the mortality due to this infection. The optimal control problem is solved by applying the Projection Stochastic Gradient Method in order to find the optimal numerical solution. Finally, we provide some numerical simulations of the controlled model

Towards a multi-agent model to prevent damage caused by cocoa mirids to cocoa pods

Co-localisées avec la Plate-Forme Intelligence Artificielle (PFIA 2019)International audienceAgriculture in general and cocoa farm in particular is one of the primary sources of income for several African countries. Although quite useful for the development of Africa, cocoa production is faced with several challenges like the diseases of cocoa trees. Mirid (Sahlbergella singularis) is the worst pest affecting cocoa production across west Africa causing 30% to 40% of damage on cocoa production. It is difficult to control the mirids’ population and its impact on the cacao production. Related works on mirids studied the mirids population as a macroscopic entity without considering local interactions of individual mirids. These models did not consider the behaviours and the environment of mirids which are essential due to their complexity. To overcome these drawbacks, this paper proposes an agent-based model of mirids considering the individual interactions of mirids within the environment. The proposed model consists of agents representing the mirids through their life cycle in cocoa farm environments. It is based on the biological and ecological partial knowledge found in the literature, and is built according to the GAIA methodology. The main assets of this model are the reproduction of the dynamics of the mirids on a cocoa pod and damage caused by them at the micro level for human users (entomologists, agricultural engineers, farmers and decision makers) to thoroughly understand the phenomena and the emergent properties outcomes.L’agriculture en général et la culture du cacao en particulier est l’une des principales sources de revenus de plusieurs pays africains. Cependant, la production du cacao est confrontée à plusieurs défis tels que les maladies et l’attaque des insectes nuisibles. Les mirides (Sahlbergella singularis) sont les insectes les plus préjudiciables à la culture du cacao en Afrique. Avec 30 à 40 % de dommages sur la production, il est difficile de contrôler la population des mirides ainsi que son impact sur la production de cacao. Les travaux précédents sur les mirides, étudient la population de cet insecte selon le point de vue macroscopique sans tenir compte des interactions locales entre les mirides. Ces modèles ne prennent pas en compte les comportements individuels des mirides et leurs interactions avec l’environnement qui sont essentiels en raison de leurs complexités. Pour remédier à ces insuffisances, le présent article propose un modèle de mirides à base d’agents prenant en compte les interactions individuelles des mirides dans leur environnement. Le modéle proposé est constitué d’agents représentant le cycle de vie du miride sur une cabosse de cacao. Il est basé sur les connaissances biologiques et écologiques du miride, et est construit selon la méthodologie GAIA. Ces modèles ainsi que leurs implémentations sont destinés à des utilisateurs tels que les entomologistes, les ingénieurs agronomes, les agriculteurs et les décideurs. Cela leur permettra de mieux comprendre les phénomènes émergents dues aux mirides ainsi que leurs propriétés