Dynamics of a Tuberculosis Outbreak Model in a Multi-scale Environment

Selain K. Kasereka

Home/Archive/arXiv

arXiv · 2411.04297

Dynamics of a Tuberculosis Outbreak Model in a Multi-scale Environment

Selain K. Kasereka

View original source ↗Read source document ↗Export metadata ↓

Abstract

Modeling and simulation approaches for infectious disease dynamics have proven to be essential tools for effective control of the spread of epidemics in the population. Among these approaches, it is obvious that compartmental mathematical models, such as SIS, SIR, SEIR, etc. are the most widely used by researchers. However, they are difficult to apply in a multi-scale environment, especially if we want to take into account the heterogeneous behaviors of individuals. The aim of this paper is to present a hybrid model in which an Equation-Based Model (EBM) of tuberculosis dynamics is coupled to an Agent-Based Model (ABM) in a two-scale environment. In this model, individuals are placed in cities considered as agents in which the dynamics of the disease is modeled by eight compartments and managed by solving a system of differential equations. Individual agents move between these cities using an ABM that controls their mobility. Considering some parametric values and assumptions, the results obtained show that human mobility has a significant impact on the spread of tuberculosis within the population. The management of population and disease dynamics at different levels (microscopic and macroscopic) testifies to the robustness of the proposed approach.

Explore related subjects

q-bio.PE math.DS

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Selain K. Kasereka. 2024-11-06. Dynamics of a Tuberculosis Outbreak Model in a Multi-scale Environment. https://arxiv.org/abs/2411.04297

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Phase transitions in microbial lineage trees

Microbial populations exhibit high cell-to-cell variability, which fundamentally shapes population behavior. A striking consequence is the existence of phase transitions, where small genetic or environmental changes trigger abrupt shifts in population dynamics. While biological phase transitions have often been proposed, connecting observed behavior to the underlying physics has remained challenging. We combine population genetics with statistical physics to show how phase transitions arise naturally in microbial populations. We highlight the existence of a first-order transition in a model of bacterial plasmid engineering and find a strict lower bound on the number of plasmids that can be stably maintained in a population.

q-bio.PE↗

arXiv2026

Phylogenetic Inference and the Stickiness of Fréchet Means, via Precise Asymptotics of an Embedded Random Walk

A well-known phenomenon in statistical analyses of populations of phylogenetic trees in the Billera-Holmes-Vogtmann space is that the topology of the Fréchet mean tree can contain multifurcations (i.e., internal nodes with more than two children), which raises the practical question of whether this reflects a population-level branching structure (hard polytomy) or merely sampling variability in the data (soft polytomy). This is an instance of the more general phenomenon of "stickiness" in non-Euclidean statistics, whereby the sample Fréchet mean in certain non-positively curved stratified spaces becomes permanently trapped in a lower-dimensional stratum. In this work, we identify a particular multidimensional random walk embedded within the Fréchet mean process, and we show that the time at which stickiness occurs is determined by the largest last-passage time above zero of the coordinates of this random walk. Using this representation, we develop a fully nonparametric procedure for estimating the probability that trifurcations in a sample Fréchet mean tree will bifurcate at some future time if more observations are collected. Lastly, we apply our methodology to a problem in phylogenetics where we consider whether an observed trifurcation in the species tree of primates, glires, and tree shrews is genuinely trifurcated at the population level.

q-bio.PE↗

arXiv2026

Coexistence coalitions in propagule disperser quasi-communities

Many natural ecosystems harbor large numbers of coexisting species competing for far fewer distinct resources, in apparent defiance of the competitive exclusion principle. Various mechanisms have been proposed to explain this apparent paradox, often pertaining to organisms with a two-stage sessile--propagule life cycle. Here we develop a stochastic model class for such propagule disperser communities that combines competition--colonization trade-offs, spatial heterogeneity, demographic stochasticity, as well as inherited trait variation, and recover several classical models as special or limiting cases. Using bifurcation analysis, we classify equilibrium coalitions near the extinction threshold and give sufficient conditions for their realization by macroscopic equilibria away from the threshold, bypassing the costly numerical computation of the actual equilibrium states. Illustrative examples examine the resulting trait distributions and coalition patterns, demonstrating the interactive effects of different coexistence mechanisms.

q-bio.PE↗