Towards hybrid stochastic modeling and simulation of complex systems in multi-scale environments with case studies on the spread of tuberculosis in Democratic Republic of the Congo

Abstract

Mathematical modeling of the spread of infectious diseases in a population has always been recognized as a powerful tool that can help decision-makers understand how a disease evolves over time. With the evolution of science and humanity, it has become evident that Mathematical models are too simplistic and have some limitations in modeling environmental phenomena, such as the spread of epidemics in a population, when they are applied without combining them with other sciences. In understanding the dynamics of epidemics in a population, the weakness of these models is their difficulty in grasping the complexity inherent in the spread of diseases in real life because, life is supported by human interactions and behaviors that are understood through networks of social and spatial interactions. Modeling the spread of epidemics which takes this reality into account requires the implementation of new tools to refine the results already obtained by mathematical models. The aim of this thesis is to explore and attempt to extend new developments in mathematical modeling of the spread of infectious diseases by proposing new tools based on mathematical models from differential equations and agent-based models from intelligent agents derived from artificial intelligence. To achieve this objective, the study starts from a comparative study of two ways of modeling and simulation of the spread of infectious diseases in the population, namely mathematical modeling and agent-based modeling with a concrete case study of the spread of tuberculosis based on data from the Democratic Republic of the Congo (DRC). Then comes a coupling study of these two approaches in a single model and its implementation in a multi-scale environment. The results show that the coupled model is more realistic compared to mathematical models generally implemented in the literature. Four case studies are presented in this thesis. Mathematical modeling based on differential equations is used in the first and second cases. The third case is based on intelligent agents model while the last one is based on the coupling of mathematical models and agent-based models. Application of implemented models to the spread of tuberculosis reveals that detection of people with latent tuberculosis and their treatment are among the actions to be taken into account in addition to those currently carried out by the Congolese health system. The models assert that the current TB situation in DRC remains endemic and that the necessary measures need to be taken to reduce the burden of TB, especially to control it, through the tuberculosis elimination strategy and its elimination in the future in accordance with the Sustainable Development Goals. Our hybrid model benefiting from the advantages of EBM and ABM confirms that taking the individual into account as a fully-fledged entity and managing their behavior gives the microscopic aspect of the model set up and brings it closer as much as possible to reality. Mathematical management of the spread of the disease in cities gives a macroscopic aspect to the model. Numerical simulations of this last model on a multi-scale virtual environment affirm that the mobility of individuals from city to city has a significant impact on the spread of tuberculosis in the population. Controlling the rate of population mobility from one city to another is one of the most important measures for large-scale disease control. This model therefore draws its richness from this dynamic at two different scales (two time scales modeling approaches: at the microscopic/individual level (ABM) and macroscopic/city level (ODE)), which gives the emergence of the model at the global level. As a result, it seems that the coupling of mathematical models to agent-based models should be applied when the dynamics of the complex system under consideration is at different scales. Based on our research results, it seems that the choice of an approach must depend on how the modeler would like to achieve the expected results. Mathematical models remain essential due to their analytical and synthetic aspect, but their coupling with intelligent agent-based models makes it possible to refine known results and thus reflect the reality of real life, because the resulting model integrate interactions of individuals and their heterogeneous behaviors that are necessary for understanding the spread of infectious diseases in the population that only mathematical models based on differential equations can not capture.