Spinned Poisson distribution with health management application.

Area of Science:

• Epidemiology
• Biostatistics
• Probability Theory

Background:

• Infectious disease data collection is often complicated by the removal of infected individuals.
• Standard probability distributions like the Poisson distribution may be inadequate for modeling such scenarios.
• Accurate incidence rate and immunity estimation is crucial for public health management during outbreaks.

Purpose of the Study:

• To derive and introduce a novel probability distribution, the spinned Poisson distribution.
• To address the limitations of existing distributions in modeling infectious disease data with case removal.
• To statistically characterize the spinned Poisson distribution and demonstrate its applicability.

Main Methods:

• Development of a new probability distribution based on modifications to the Poisson process.
• Theoretical derivation of the statistical properties of the spinned Poisson distribution.
• Application and illustration of the distribution using historical smallpox incidence data from Abakaliki, Nigeria.

Main Results:

• The spinned Poisson distribution was successfully derived and its properties were established.
• The new distribution provides a more appropriate model for infectious disease incidence when infected cases are removed.
• Analysis of smallpox data demonstrated the practical utility of the spinned Poisson distribution.

Conclusions:

• The spinned Poisson distribution offers a statistically sound approach for analyzing infectious disease data with inherent case removal.
• This novel distribution enhances the accuracy of incidence rate and immunity estimations in epidemiological studies.
• The findings have implications for public health surveillance and disease management strategies.