Plague disease model with weather seasonality

Area of Science:

• Epidemiology
• Mathematical Biology
• Disease Modeling

Background:

• Plague is a severe bacterial infection caused by Yersinia pestis.
• Understanding disease transmission dynamics is crucial for public health interventions.
• Seasonal variations can significantly impact the spread of infectious diseases.

Purpose of the Study:

• To investigate a plague disease model that includes the effect of seasonal weather variations on transmission.
• To analyze the conditions for disease-free equilibrium and the existence of periodic solutions.
• To determine the global stability of periodic solutions for the plague model.

Main Methods:

• Mathematical modeling of disease transmission.
• Analysis of differential equations to determine equilibrium and stability.
• Application of existence-uniqueness theorems.
• Numerical simulations to illustrate model behavior.

Main Results:

• A globally asymptotically stable disease-free equilibrium exists when the periodic reproduction number (R_T) is greater than one.
• The existence of at least one positive periodic solution is proven when R_T > 1.
• Conditions for the global stability of periodic solutions were established.

Conclusions:

• Seasonal weather variations influence plague transmission dynamics.
• The model predicts conditions under which plague may persist periodically.
• Numerical simulations support the theoretical findings on plague disease dynamics.