Epidemic Modeling Using Differential Equations
In this paper, I derive a simple differential equation model to visualize the spread of disease during an epidemic. I estimate the number of susceptible individuals using the rate of change of susceptible individuals, which depends on the number of infectious contacts an infected individual makes per day while they remain contagious. Similarly, I use the rate of change of recovered individuals to estimate the number of recovered individuals, which depends on the fraction of infected individuals who cease being contagious at a given point in time. To estimate the number of infected individuals at a given time, I use the rate of change, which depends on the rate of change of both susceptible and recovered individuals. Further, using open-source Python code, I plot data from the novel coronavirus (COVID-19) pandemic provided by Johns Hopkins University, and use it to calculate the mortality rate, recovery rate, and effective contact rate. These parameters can be useful for predictive modeling of epidemic conditions to inform preventative measures that may mitigate risk in times of rapid disease spread, such as the COVID-19 pandemic.