Nonhomogeneous birth and death models for epidemic outbreak data

Area of Science:

• Epidemiology
• Biostatistics
• Mathematical Modeling

Background:

• Epidemic disease outbreaks pose significant public health challenges.
• Accurate statistical modeling is crucial for understanding disease dynamics and implementing control strategies.

Purpose of the Study:

• To propose generalized nonlinear models for statistically analyzing epidemic disease outbreaks.
• To incorporate data dependence, early outbreak stages, delayed registration of infected individuals, and the impact of control measures into epidemic models.

Main Methods:

• Utilizing nonhomogeneous birth or death processes to handle data dependence.
• Employing a susceptible-infective-removed (SIR) model for the initial outbreak phase.
• Linking disease prevalence to censored infection times, leading to the Burr family of distributions.
• Modifying survival functions with a final-size parameter to account for epidemic control measures.

Main Results:

• The proposed generalized nonlinear models provide a flexible framework for epidemic modeling.
• The models successfully incorporate complex factors such as control measures and delayed reporting.
• Application to swine fever, foot-and-mouth disease, and avian influenza outbreaks demonstrates model utility.

Conclusions:

• Generalized nonlinear models offer a robust approach to statistically modeling epidemic disease outbreaks.
• These models enhance understanding of disease dynamics influenced by interventions.
• The methodology is validated through successful application to significant historical epidemics.