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Mathematical Modeling of Polio Transmission Dynamics with the Impact of Immigration and Delay in Vaccination

Benneth Peter and Eli Innocent Cleopas

Abstract

Poliomyelitis remains a significant global health concern despite substantial progress in its eradication through vaccination. This study focused on the resurgence of polio in regions experiencing high immigration rates and delays in vaccination coverage. Polio, caused by the poliovirus, primarily spreads through the fecal-oral route and can result in permanent paralysis or death. Although both inactivated and oral polio vaccines have proven effective, challenges such as vaccine-derived virus transmission and insufficient intestinal immunity from IPV persist. This study aims to formulate a comprehensive mathematical model that incorporates immigration as a source of new susceptible individuals and integrates delay differential equations to represent postponed vaccination. Through this model, we quantify the combined effects of immigration and delayed vaccination on polio outbreak dynamics, including the timing and magnitude of transmission. Furthermore, the model evaluates the stability of the disease-free equilibrium and suggests strategies for mitigating outbreak risks through timely vaccination and improved public health responses. By addressing the limitations of existing models, this research provides critical guidance for policymakers and health professionals working toward the global eradication of polio especially in regions facing public health infrastructure challenges and high population mobility. The simulated result further reveal that increased vaccination delays or longer relaxation times can induce oscillatory behavior in infection dynamics, suggesting the urgent need for prompt immunization efforts.

References

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