An epidemiologist models the spread of a virus in a city of 2 million people. Initially, 0.1% are infected. Each day, the number of infected individuals increases by 15% of the current infected count, while 0.5% of infected recover. After 3 days, how many people are infected (rounded to the nearest whole number)?

Epidemiological Model: Simulating Virus Spread Over 3 Days in a 2 Million City

Understanding how infectious diseases spread is crucial for public health planning. An epidemiologist recently modeled the progression of a virus in a city of 2 million people. Using a simplified daily growth and recovery model, we analyze how infection levels evolve over three days—starting from a small, initial cluster.

Initial Infection Count

The city has 2,000,000 residents. Initially, only 0.1% are infected:
Initial infected = 2,000,000 × 0.001 = 2,000 people

Understanding the Context

Each day, two key factors influence the count:

Infection growth: The number of infected individuals increases by 15% of the current infected count.
Recovery: Simultaneously, 0.5% of infected individuals recover and move to the recovered group.

Let’s simulate day-by-day to determine total infected after 3 days, with values rounded to the nearest whole number.

Day-by-Day Breakdown

An epidemiologist models the spread of a virus in a city of 2 million people. Initially, 0.1% are infected. Each day, the number of infected individuals increases by 15% of the current infected count, while 0.5% of infected recover. After 3 days, how many people are infected (rounded to the nearest whole number)?

Key Insights

Day 0 (Initial):

Infected at start: 2,000

Day 1:

Infection growth:
Increase = 2,000 × 0.15 = 300
New infected before recovery = 2,000 + 300 = 2,300
Recoveries:
Recoveries = 2,000 × 0.005 = 10
Total infected after Day 1:
2,300 – 10 = 2,290

Day 2:

Infection growth:
Increase = 2,290 × 0.15 = 343.5 ≈ 344
Total before recovery = 2,290 + 344 = 2,634
Recoveries:
Recoveries = 2,290 × 0.005 = 11.45 ≈ 11
Total infected after Day 2:
2,634 – 11 = 2,623

Day 3:

Infection growth:
Increase = 2,623 × 0.15 = 393.45 ≈ 393
Total before recovery = 2,623 + 393 = 3,016
Recoveries:
Recoveries = 2,623 × 0.005 = 13.115 ≈ 13
Total infected after Day 3:
3,016 – 13 = 3,003

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Final Thoughts

Final Result

After 3 days, the number of infected individuals is approximately 3,003, rounded to the nearest whole number.

Using the Formula for Insight

This process mirrors exponential growth with a net daily multiplier:
Each day, infected individuals grow by 15% (×1.15), while recoveries reduce the count by 0.5% (×0.995). The net daily factor is:
1.15 × 0.995 ≈ 1.14425

Using exponential modeling:
Infected after 3 days = 2,000 × (1.14425)³ ≈ 2,000 × 1.503 ≈ 3,006
Approximation confirms the iterative result: rounding differences explain the slight variance due to discrete daily adjustments.

Conclusion

In a city of 2 million, starting with a modest 2,000 infected and applying 15% daily growth offset by 0.5% recovery yields approximately 3,003 infected individuals after 3 days. This model highlights how quickly early outbreaks can escalate—even with partial recovery—emphasizing the importance of timely intervention and surveillance.

For public health planners, numbers like these inform resource allocation, testing strategies, and community outreach to curb transmission before exponential spread becomes unmanageable.

Keywords: epidemiologist, virus spread model, 2 million city, daily infection growth 15%, recovery rate 0.5%, infectious disease simulation, public health modeling