public ActionResult Index(String search)
{
    if (HttpContext.Request.Headers["X-Requested-With"] == "XMLHttpRequest")
        return PartialView("_IndexGrid", repository.GetPeople(search));

    return View();
}

<input id="GridSearch" />

@Html.AjaxGrid(Url.Action("Index"))

<script>
    document.getElementById("GridSearch").addEventListener("input", function() {
        const grid = new MvcGrid(document.querySelector(".mvc-grid"));

        grid.url.searchParams.set("search", this.value);

        grid.reload();
    });
</script>

@model IQueryable<Person>

@* Should only include grid declaration *@

@(Html
    .Grid(Model)
    .Build(columns =>
    {
        columns.Add(model => model.Name).Titled("Name");
        columns.Add(model => model.Surname).Titled("Surname");
        columns.Add(model => model.MaritalStatus).Titled("Marital status");

        columns.Add(model => model.Age).Titled("Age");
        columns.Add(model => model.Birthday).Titled("Birthday").Formatted("{0:d}");
        columns.Add(model => model.IsWorking).Titled("Employed");
    })
    .Empty("No data found")
    .Sortable()
)