$\"\"$

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A single infected individual enters a community of $\"\"$ suspectible individuals.

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Let $\"\"$ be the number of newly infected individuals in time $\"\"$ .

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The value of $\"\"$ is $\"\"$ .

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$\"\"$ .

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Solve the integral $\"\"$ by using partial fractions.

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$\"\"$

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Compare the $\"\"$ coefficient.

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$\"\"$

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Compare the constant.

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Initial condition: $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ as a function of $\"\"$ is $\"\"$ .