Cross immunity protection and antibody-dependent enhancement in a distributed delay dynamic model

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• Dengue fever is a significant public health concern in tropical and subtropical regions.
• Mathematical modeling of dengue transmission faces challenges due to complex factors like multi-serotypes and cross-immunity.

Purpose of the Study:

• To develop and analyze a mathematical model for dengue transmission dynamics.
• To incorporate and investigate the impact of time-delayed acquired cross-immunity and antibody-dependent enhancement (ADE).

Main Methods:

• Development of a system of integro-differential equations (IDE) to model dengue spread.
• Qualitative analysis of the model, including stability analysis of steady states.
• Construction of a Lyapunov functional to establish global dynamics.
• Numerical simulations to explore bifurcation structures and parameter effects.

Main Results:

• The stability of epidemiologically significant steady solutions was determined by the basic reproduction number and invasion reproduction number.
• Global dynamics of the disease were established using a Lyapunov functional.
• Numerical experiments demonstrated bifurcation structures, indicating periodic oscillations under specific ADE parameter values.

Conclusions:

• The proposed IDE model effectively captures key dengue transmission characteristics, including cross-immunity and ADE.
• The model provides insights into disease stability and the potential for periodic outbreaks influenced by ADE.
• Mathematical modeling remains a crucial tool for understanding and managing dengue fever dynamics.