WordPress search page pagination displaying but not functional

Answer provided in the comments:

global $wp_query;
$big = 999999999; // need an unlikely integer
$pagination_args = array(
    'base'      => str_replace($big, '%#%', esc_url(get_pagenum_link($big))),
    'format'    => '?paged=%#%',
    'current'   => max( 1, get_query_var('paged') ),
    'mid_size'  => 1,
    'total'     => $wp_query->max_num_pages
);
if(have_posts()):
    while(have_posts()):
        the_post();
        //individual search result
    endwhile;
    wp_reset_postdata();
    echo paginate_links($pagination_args);
endif;