Understanding the effect of vector dynamics in epidemic models using center manifold analysis

Area of Science:

• Epidemiology
• Mathematical Modeling
• Vector-Borne Diseases

Background:

• Vector-borne diseases involve pathogens transmitted by vectors like mosquitoes.
• Mosquitoes have significantly faster life cycles and reproductive rates than humans.
• This disparity creates different epidemiological timescales between hosts and vectors.

Purpose of the Study:

• To investigate if slower human epidemiology can dominate faster mosquito epidemiology in vector-borne diseases.
• To determine the extent to which mosquito dynamics are influenced by human disease patterns.
• To assess the essentiality of human timescale dynamics for understanding disease data.

Main Methods:

• Utilized a mathematical model (SIRUV) incorporating susceptible, infected, and recovered humans (S, I, R).
• Included susceptible and infected mosquitoes (U, V) in the model.
• Analyzed the model to understand the "slaving" of fast mosquito timescales by slower human timescales.

Main Results:

• The study found that human epidemiological timescales can indeed "slave" the faster mosquito timescales.
• The dynamics of human disease are largely determined by the human timescale.
• Mosquito dynamics introduce only minor perturbations to the overall human disease patterns.

Conclusions:

• Human disease data is predominantly essential for understanding vector-borne disease epidemiology.
• The slower human timescale is the primary driver, with faster mosquito dynamics having a limited impact.
• These findings align with previous models (SISUV) and represent a general feature of vector-borne diseases.