Global asymptotic stability in a pseudorabies virus model with age structure
Yining Chen1, Yuhua Long1, Jianshe Yu1
1College of Mathematics and Information Sciences, Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, People's Republic of China.
Infectious Disease Modelling
|August 11, 2023
Summary
This study models pseudorabies virus (PRV) spread in pigs, revealing a critical threshold. Below this, PRV persists in piglets but not adults; above it, the disease becomes endemic in the entire population.
Area of Science:
- Veterinary Virology
- Mathematical Epidemiology
- Swine Disease Dynamics
Background:
- Pseudorabies virus (PRV), or suid herpesvirus 1 (SuHV1), is a highly contagious pathogen causing substantial economic losses in the global swine industry.
- Understanding PRV transmission dynamics is crucial for effective disease control and prevention strategies in pig populations.
Purpose of the Study:
- To develop and analyze an age-structured mathematical model for pseudorabies virus transmission.
- To investigate the impact of disease-related mortality and vertical transmission on PRV dynamics.
- To identify conditions for disease persistence and eradication in different age groups of swine.
Main Methods:
- Formulation of an age-structured compartmental model for PRV transmission.
- Analysis of the model's equilibria and their stability using mathematical techniques.
- Determination of a threshold parameter governing disease persistence.
Main Results:
- A critical threshold was identified, determining the stability of the disease-free equilibrium.
- When the threshold condition is met (), PRV is endemic in piglets but clears in adults.
- Above the threshold (), a unique, globally stable endemic equilibrium exists, indicating widespread disease.
Conclusions:
- The age structure and transmission routes significantly influence PRV's epidemiological behavior.
- The model provides insights into age-dependent disease dynamics, crucial for targeted intervention strategies.
- Mathematical modeling is a valuable tool for understanding and managing viral diseases in livestock.
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