Models for diseases with vertical transmission and nonlinear population dynamics

Area of Science:

• Epidemiology
• Mathematical Biology
• Population Dynamics

Background:

• Vertical transmission is crucial for understanding disease spread from parents to offspring.
• Existing models often assume birth rates are directly proportional to population size.
• Nonlinear population dynamics and finite carrying capacities are important factors often overlooked.

Purpose of the Study:

• To investigate vertical transmission models incorporating nonlinear population dynamics.
• To analyze the stability of disease equilibria under conditions of finite carrying capacity.
• To explore scenarios where overall birth rates are independent of the infective population size.

Main Methods:

• Development of mathematical models for vertical disease transmission.
• Analysis of population dynamics with nonlinear growth and carrying capacity.
• Stability analysis of equilibrium points in the disease model.

Main Results:

• Identified conditions for disease persistence or extinction in populations with limited growth.
• Demonstrated the impact of nonlinear birth rates on disease dynamics.
• Characterized the stability of equilibria when birth rates are independent of the infected population.

Conclusions:

• Nonlinear population dynamics significantly influence vertical transmission patterns.
• Finite carrying capacity and independent birth rates can alter disease stability outcomes.
• This research provides a more realistic framework for studying endemic diseases.