Optimal vaccine allocation during the mumps outbreak in two SIR centres

Area of Science:

• Epidemiology
• Mathematical Modeling
• Public Health

Background:

• Mumps outbreaks pose significant public health challenges, impacting workforce productivity.
• Migration between populations complicates disease control efforts.
• Resource allocation, like vaccine distribution, is critical during epidemics.

Purpose of the Study:

• To determine the optimal vaccine sharing strategy between two susceptible, infected, removed (SIR) centers.
• To minimize the total number of lost working days during a mumps outbreak.
• To analyze how migration and vaccine availability influence optimal allocation.

Main Methods:

• Utilized a Susceptible-Infected-Removed (SIR) compartmental model.
• Incorporated migration fluxes of susceptible and infected individuals.
• Defined optimality by minimizing the integral of infected individuals over time ($Q=\int _0^{t_f}I(t)\,{\textrm{d}}t$).

Main Results:

• The optimal vaccine allocation strategy is dependent on key model parameters.
• The amount of available vaccine ($V$) significantly influences the distribution strategy.
• Migration patterns affect the required vaccine distribution for effective control.

Conclusions:

• Effective mumps outbreak management requires tailored vaccine sharing strategies.
• Understanding migration dynamics is crucial for optimizing resource allocation in public health interventions.
• The study provides a framework for optimal vaccine distribution under realistic epidemiological conditions.