Loading scripts on specific pages using PHP in footer.php

You should be using wp_enqueue_script rather than putting script tags directly in template files:

function wpa61143_enqueue_scripts() {
    if( is_page( 'home' ) ) :
        wp_enqueue_script( 
            'jcarousel',
            get_template_directory_uri() . '/scripts/jquery.jcarousel.min.js',
            array( 'jquery' ),
            null,
            true,
        );
    elseif( is_single() ) :
        // enqueue scripts for single
    elseif( ! is_page_template('modelPages.php') ) :
        // enqueue scripts for other
    endif;
}    

add_action( 'wp_enqueue_scripts', 'wpa61143_enqueue_scripts' );