An SIQ delay differential equations model for disease control via isolation.

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• Infectious diseases pose significant global threats.
• Isolation of infected individuals is a key control strategy when preventive healthcare is limited.
• Mathematical modeling can inform disease control interventions.

Purpose of the Study:

• To analyze the impact of isolation on infectious disease dynamics.
• To develop a mathematical model for studying disease control through isolation.
• To determine the minimum isolation response required to contain an outbreak.

Main Methods:

• A system of delay differential equations was developed to model infectious disease spread and isolation.
• The model was analyzed using the geometric theory of semi-flows.
• Parameters were calibrated based on the fraction of infectious individuals isolated and the speed of isolation.

Main Results:

• The study identifies the minimum isolation response necessary to curb an incipient infectious disease outbreak.
• The model predicts the endemic state of the disease if the outbreak is not contained.
• The effectiveness of isolation strategies is quantitatively assessed.

Conclusions:

• Mathematical modeling provides crucial insights into optimizing infectious disease control measures.
• Strategic and timely isolation is critical for preventing widespread endemic disease.
• This research offers a framework for public health policy regarding infectious disease management.