Generating a sitemap for a custom model

The steps I ended up using were as follows, and the comments and answers so far got me started in the right direction.

First I added a row to the "sitemap" table. Since we have multi-store set up, and because I want to keep my module store agnostic, I didn't hard code this INSERT into a MySQL migration, but just ran it on the store manually:

INSERT INTO sitemap (sitemap_type, sitemap_filename, sitemap_path, store_id)
    VALUES ('people', 'people.xml', '/sitemap/', 2);

Then I overwrote the Mage_Sitemap_Model_Sitemap model inside the global/models section in my own module's config.xml file:

<global>
    <models>
        <sitemap>
            <rewrite>
                <sitemap>Mymod_People_Model_Sitemap</sitemap>
            </rewrite>
        </sitemap>
    </models>
</global>

This overwrites any calls to Mage_Sitemap_Model_Sitemap site-wide with my custom model, but I didn't want to copy and paste too much code there. Using Petar Dzhambazov's suggestion, I used a conditional to defer to the parent class unless the sitemap_type is "people".

class Mymod_People_Model_Sitemap extends Mage_Sitemap_Model_Sitemap
{
    const PAGE_REFRESH_FREQUENCY = 'weekly';
    const PAGE_PRIORITY = '1.0';

    public function generateXml()
    {
        if ($this->getSitemapType() != 'people') {
            return parent::generateXml();
        }

        $io = new Varien_Io_File();
        $io->setAllowCreateFolders(true);
        $io->open(array('path' => $this->getPath()));

        if ($io->fileExists($this->getSitemapFilename()) && !$io->isWriteable($this->getSitemapFilename())) {
            Mage::throwException(Mage::helper('sitemap')->__('File "%s" cannot be saved. Please, make sure the directory "%s" is writeable by web server.', $this->getSitemapFilename(), $this->getPath()));
        }

        $io->streamOpen($this->getSitemapFilename());

        $io->streamWrite('<?xml version="1.0" encoding="UTF-8"?>' . "\n");
        $io->streamWrite('<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">');

        $storeId = $this->getStoreId();
        $date    = Mage::getSingleton('core/date')->gmtDate('Y-m-d');
        $baseUrl = Mage::app()->getStore($storeId)->getBaseUrl(Mage_Core_Model_Store::URL_TYPE_LINK);

        /**
         * Generate people sitemap
         */
        $changefreq = Mymod_People_Model_Sitemap::PAGE_REFRESH_FREQUENCY;
        $priority   = Mymod_People_Model_Sitemap::PAGE_PRIORITY;
        $collection = Mage::getModel('people/person')->getCollection();
        foreach ($collection as $item) {
            $xml = sprintf('<url><loc>%s</loc><lastmod>%s</lastmod><changefreq>%s</changefreq><priority>%.1f</priority></url>',
                htmlspecialchars($item->getUrl()),
                $date,
                $changefreq,
                $priority
            );
            $io->streamWrite($xml);
        }
        unset($collection);

        $io->streamWrite('</urlset>');
        $io->streamClose();

        $this->setSitemapTime(Mage::getSingleton('core/date')->gmtDate('Y-m-d H:i:s'));
        $this->save();

        return $this;
    }
}

Is there a better way, that avoids copying and pasting so much from the parent class?