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

Selain K. Kasereka

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.

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

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.

Paper Structure

This paper contains 18 sections, 1 equation, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Description of the Mathematical Model
  3. Description of the ABM using ODD Protocol
  4. Overview
  5. Design Concept
  6. Details
  7. Simulations of the Hybrid Model
  8. Parameters used in the Model
  9. Numerical Simulation
  10. Simulation with a High Mobility Rate for all Individuals
  11. Simulation with Basic Parameters and Consideration of a Low Mobility Rate for $I, L_e$ and $L_f$ Individuals
  12. Runtime Evaluation
  13. Benchmark Models
  14. Discussion of the Results and Recommendations
  15. General Discussion
  16. ...and 3 more sections

Figures (8)

  • Figure 1: Compartmental model of TB transmission.
  • Figure 2: Presentation of the environment with 6 cities (circles) interconnected via a hub. (a) simulation at time $t=0$, (b) simulation at time $t=79$, (c) simulation at time $t=262$, (d) simulation at time $t=328$. The concentration of the red color of the city is proportional to the level of infectivity of the city.
  • Figure 3: Evolution of the model for all cities considered globally
  • Figure 4: Evolution of the model with 6 cities (circles) interconnected via a hub. (a) presentation of the TB dynamics in city 1, (b) for city 2, (c) for city 3 and (d) for city 4.
  • Figure 5: Environment with 6 cities (circles) interconnected via a hub. (a) simulation at time $t=0$, (b) simulation at time $t=79$, (c) simulation at time $t=262$, (d) simulation at time $t=328$. The concentration of the red color of the city is proportional to the level of infectivity of the city.
  • ...and 3 more figures