A mathematical model for coupling within-host and between-host dynamics in an environmentally-driven infectious
Zhilan Feng1, Jorge Velasco-Hernandez, Brenda Tapia-Santos
1Department of Mathematics, Purdue University, West Lafayette, Indiana, USA. zfeng@math.purdue.edu
Mathematical Biosciences
|October 9, 2012
Summary
This study introduces a new model linking within- and between-host dynamics for Toxoplasma gondii infections. New reproductive numbers reveal how parasite transmission and stability are determined, potentially showing backward bifurcation.
Area of Science:
- Mathematical modeling
- Infectious disease dynamics
- Parasitology
Background:
- Toxoplasma gondii infection involves complex within- and between-host dynamics.
- Environmental contamination and inoculum size influence host acquisition.
- Different time scales characterize within- and between-host processes.
Purpose of the Study:
- To develop a novel mathematical model integrating within- and between-host dynamics for T. gondii.
- To analyze the impact of environmental interactions and inoculum size on infection.
- To define and investigate new reproductive numbers for coupled host-parasite systems.
Main Methods:
- Singular perturbation argument to decouple fast (within-host) and slow (between-host) systems.
- Definition and analysis of novel reproductive numbers for isolated and coupled dynamics.
- Stability analysis of infection-free and endemic equilibrium points.
Main Results:
- The model successfully links within- and between-host dynamics for T. gondii.
- Reproductive numbers for the between-host system are naturally dependent on within-host parameters.
- The defined reproductive numbers dictate the stability of equilibrium points.
- The model suggests the possibility of a backward bifurcation.
Conclusions:
- The developed model provides a framework for understanding T. gondii transmission dynamics.
- New reproductive numbers are crucial for predicting infection persistence and stability.
- The interplay between within- and between-host processes is essential for disease dynamics and can lead to complex outcomes like backward bifurcation.
More Related Videos
09:02An Experimental Model to Study Tuberculosis-Malaria Coinfection upon Natural Transmission of Mycobacterium tuberculosis and Plasmodium berghei
Published on: February 17, 2014
07:56Generation of a Bovine Primary Enteroid-Derived Two-Dimensional Monolayer Culture System for Applications in Translational Biomedical Research
Published on: April 5, 2024
Related Concept Videos
01:25Modeling with Differential Equations
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
00:57Population Growth
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
01:18Models of Health Promotion and Illness Prevention II
The person's health status fluctuates continually, varying from being in good health to becoming ill and returning to being healthy. To understand the concept of illness prevention, there are two models. First, the health-illness continuum model is a graphic representation of an individual's wellness. It states that a person is considered healthy in the absence of physical disease and the presence of good emotional health.
The agent-host-environment model states that disease results from...
The agent-host-environment model states that disease results from...
01:21Causality in Epidemiology
Causality or causation is a fundamental concept in epidemiology, vital for understanding the relationships between various factors and health outcomes. Despite its importance, there's no single, universally accepted definition of causality within the discipline. Drawing from a systematic review, causality in epidemiology encompasses several definitions, including production, necessary and sufficient, sufficient-component, counterfactual, and probabilistic models. Each has its strengths and...
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
01:20Infection
When a pathogen enters the body and reproduces, it can cause an infection, damage body cells, and cause illness symptoms that eventually lead to disease. Therefore, its prevention requires breaking the chain of infection.
The chain begins with pathogens: bacteria, viruses, fungi, prions, or parasites such as protozoa helminths. These can be present on the skin as transient or resident flora, or they can be acquired from the environment. Identifying and treating the type of infection and...
The chain begins with pathogens: bacteria, viruses, fungi, prions, or parasites such as protozoa helminths. These can be present on the skin as transient or resident flora, or they can be acquired from the environment. Identifying and treating the type of infection and...