SIRI+Q model with a limited capacity of isolation

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• Reinfectious diseases pose significant public health challenges.
• Effective disease control strategies are essential to mitigate epidemic consequences.
• Limited resources, such as isolation capacity, can complicate disease management.

Purpose of the Study:

• To analyze an SIRI+Q model incorporating limited isolation capacity for a reinfectious disease.
• To investigate the relationship between isolation capacity and epidemic outcomes.
• To determine how endemicity and final epidemic size are influenced by isolation capacity.

Main Methods:

• Construction and analysis of a piecewise smooth system of ordinary differential equations.
• Derivation of conditions for isolation capacity to reach its limit.
• Mathematical investigation of endemicity and epidemic size dependence on isolation capacity.

Main Results:

• The study derives conditions under which isolation capacity is reached at finite time.
• It demonstrates that limited isolation capacity can lead to endemic disease.
• The research quantifies the impact of isolation capacity on endemicity and final epidemic size.

Conclusions:

• Isolation capacity is a critical factor in controlling the spread of reinfectious diseases.
• The mathematical model provides theoretical insights into the challenges of disease control with limited resources.
• Effective disease management requires careful consideration of resource limitations and their impact on epidemic trajectories.