Optimal control problem arising from COVID-19 transmission model with rapid-test.

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• The Coronavirus (COVID-19) pandemic necessitates effective public health interventions.
• Mathematical modeling is crucial for understanding and controlling infectious disease outbreaks.
• Rapid testing is a key intervention strategy for managing COVID-19.

Purpose of the Study:

• To develop a mathematical model for COVID-19 incorporating rapid testing as an intervention.
• To analyze the model's mathematical and epidemiological properties, including stability and bifurcation.
• To assess the effectiveness and cost-efficiency of rapid testing for COVID-19 eradication.

Main Methods:

• Non-linear differential equations were used to model COVID-19 dynamics.
• The model's biologically feasible region and boundedness were established.
• Sensitivity analysis was performed using three normalization techniques.
• Optimal control theory was applied to evaluate time-dependent rapid testing strategies.
• Numerical simulations were conducted using MATLAB and SBToolbox.
• COVID-19 incidence data from China, Italy, and Pakistan were forecasted.

Main Results:

• A forward bifurcation was observed when the basic reproduction number equals unity.
• Sensitivity analysis indicated the significant potential of rapid testing for COVID-19 eradication.
• Time-dependent rapid testing interventions effectively suppressed COVID-19 spread with low intervention costs.
• Forecasts suggest Italy shows a decreasing trend, while Pakistan approaches its COVID-19 peak.

Conclusions:

• Rapid testing is a viable and cost-effective strategy for controlling the COVID-19 pandemic.
• Mathematical modeling provides valuable insights into optimizing intervention programs.
• The study offers a framework for forecasting disease trends and guiding public health policy.