A compartmental epidemic model with age stratification for insurance premium calculation

Shirali Kadyrov; Gauhar Kayumova; Asilbek Yallaboyev; Bizhigit Sagidolla; Shirali Kadyrov; Gauhar Kayumova; Asilbek Yallaboyev; Bizhigit Sagidolla

doi:10.3934/mbe.2025114

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 12: 3088-3106. doi: 10.3934/mbe.2025114

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A compartmental epidemic model with age stratification for insurance premium calculation

1.
New Uzbekistan University, Tashkent 100000, Uzbekistan
2.
SDU University, Kaskelen 040900, Kazakhstan

Received: 16 June 2025 Revised: 27 August 2025 Accepted: 04 September 2025 Published: 17 October 2025

This paper develops a mathematical framework for life and health insurance premium calculation under epidemic conditions, incorporating age-structured population dynamics and disease compartments. We proposed a compartmental epidemic model with three age groups and four states (susceptible, infectious, recovered, deceased) to reflect heterogeneity in disease progression and risk exposure. The model captures differential mortality and morbidity risks across age groups and infection states, enabling dynamic adjustment of insurance premiums. By integrating actuarial principles with epidemic-driven transition probabilities, we derived explicit premium formulas and validated them through numerical simulations. Our results demonstrate that age stratification and detailed infection stages significantly impact premium pricing, particularly for older populations with higher mortality risks. Sensitivity analysis reveals that recovery and mortality rates are key drivers of premium variability. The framework provides insurers with a robust tool for pandemic risk assessment, ensuring solvency while maintaining affordability.
- epidemic modeling,
- age stratification,
- health insurance,
- premium calculation,
- actuarial principles,
- SIRD model,
- hospitalization costs,
- parameter estimation,
- sensitivity analysis,
- disease dynamics,
- genetic algorithm
Citation: Shirali Kadyrov, Gauhar Kayumova, Asilbek Yallaboyev, Bizhigit Sagidolla. A compartmental epidemic model with age stratification for insurance premium calculation[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 3088-3106. doi: 10.3934/mbe.2025114

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Abstract

This paper develops a mathematical framework for life and health insurance premium calculation under epidemic conditions, incorporating age-structured population dynamics and disease compartments. We proposed a compartmental epidemic model with three age groups and four states (susceptible, infectious, recovered, deceased) to reflect heterogeneity in disease progression and risk exposure. The model captures differential mortality and morbidity risks across age groups and infection states, enabling dynamic adjustment of insurance premiums. By integrating actuarial principles with epidemic-driven transition probabilities, we derived explicit premium formulas and validated them through numerical simulations. Our results demonstrate that age stratification and detailed infection stages significantly impact premium pricing, particularly for older populations with higher mortality risks. Sensitivity analysis reveals that recovery and mortality rates are key drivers of premium variability. The framework provides insurers with a robust tool for pandemic risk assessment, ensuring solvency while maintaining affordability.

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