Stochastic models of a parasitic infection, exhibiting three basic reproduction ratios

Related Experiment Video

Updated: Oct 5, 2026

Oral Bacterial Infection and Shedding in Drosophila melanogaster
09:32

Oral Bacterial Infection and Shedding in Drosophila melanogaster

Published on: May 31, 2018

C J Luchsinger1

  • 1Abteilung Angewandte Mathematik, Universität Zürich, Switzerland. cl@luchsinger-mathematics.ch

Journal of Mathematical Biology
|August 4, 2001
PubMed

Insights

This study explores two stochastic models of parasitic infection, one linear and one non-linear, incorporating host mortality. Findings reveal complex infection dynamics where the basic reproduction ratio alone doesn't predict epidemic growth or extinction.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Parasitology

Background:

  • Parasitic infections pose significant public health challenges.
  • Stochastic models are crucial for understanding disease dynamics and transmission.
  • Existing models may not fully capture complex host-parasite interactions.

Purpose of the Study:

  • To investigate two related stochastic models of parasitic infection.
  • To analyze the influence of density-dependent constraints and host mortality.
  • To determine factors governing infection growth and extinction.

Main Methods:

  • Development and analysis of a linear and a non-linear stochastic model.
  • Inclusion of host mortality and density-dependent transmission.
  • Application of martingale and coupling methods for proofs.

Main Results:

  • The basic reproduction ratio (R0) is insufficient to predict infection dynamics in all scenarios.
  • Three distinct parameter regions dictate model behavior.
  • Model outcomes depend on specific parameter combinations, not solely R0.

Conclusions:

  • Parasitic infection dynamics are complex and influenced by multiple factors.
  • R0 requires careful interpretation in density-dependent, host-mortality scenarios.
  • Further research using these models can inform control strategies.

More Related Videos

Protocol for Production of a Genetic Cross of the Rodent Malaria Parasites13:39

Protocol for Production of a Genetic Cross of the Rodent Malaria Parasites

Published on: January 3, 2011

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness12:21

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness

Published on: September 28, 2022

Related Concept Videos

Modeling with Differential Equations01:25

Modeling 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...
Population Growth00:57

Population 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.However, realistic environmental conditions limit the number of...
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
Microbial Interactions: Parasitism01:22

Microbial Interactions: Parasitism

Parasitism is a form of microbial interaction in which parasitic microbes exploit a host organism for nutrients and shelter, often at the host's expense. Unlike mutualistic relationships, where both organisms benefit, parasitism benefits only the parasite and harms the host.Classification of ParasitesMicrobial parasites are broadly classified based on their location relative to the host.Ectoparasites remain on the host’s surface, such as the skin or outer tissues, drawing nutrients...
Malaria01:29

Malaria

Malaria pathogenesis in humans reflects a delicate interplay between parasite biology and host response. Clinical illness reflects a host’s immune response to the parasite’s asexual replication cycle, which is often asymptomatic in individuals with partial immunity. From the parasite's perspective, transmission between mosquito and human with minimal host pathology is evolutionarily advantageous. Among the six Plasmodium species infecting humans, P. falciparum and P. vivax dominate in global...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic 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)...