Optimal Control of an Infectious Disease Model in Case of Imperfect Testing

In this work, we study the spread of a communicable disease using an SIR model that includes the effect of imperfect testing. The model is extended by adding birth and natural death rates, and it uses a standard incidence rate to describe disease dynamics over a long period, rather than just during an outbreak. We find the disease-free equilibrium and the basic reproduction number to analyze the system’s stability. To control transmission and testing rates, we set up an optimal control problem to find the best values. To do this, we simulate three different control problems: one with only isolation, one with only testing, and one with both. We see that reducing contact between susceptible and infected people is very important, along with having an effective testing strategy.