Remove the list of people to show with the search engine

I need that I do not see the list of all the people when I enter the index view, but when I search the search engine I see the results. Thank you in advance.

Controller

public ActionResult Index(string option, string search)
    {

        //if a user choose the radio button option as Subject  
        if (option == "Cedula")
        {
            //Index action method will return a view with a student records based on what a user specify the value in textbox  
            return View(db.tg04Personas.Where(x => x.personaCedula == search || search == null).ToList());
        }
        else if (option == "Ruc")
        {
            return View(db.tg04Personas.Where(x => x.personaRuc == search || search == null).ToList());
        }
        else  
        {
            return View(db.tg04Personas.Where(x => x.personaNombre.StartsWith(search) || search == null).ToList());
        }
    }

View

  @using (Html.BeginForm("Index", "tg04Personas", FormMethod.Get))
  {
//the following are search options
<b> Buscar por: </b>
@Html.RadioButton("option", "Nombre") <text>Nombre</text> 
@Html.RadioButton("option", "Cedula") <text> Cédula </text>
@Html.RadioButton("option", "Ruc")<text>Ruc</text> 
@Html.TextBox("search")
<input type = "submit" name = "submit" value = "Search"/>
}

   <table class="table">
<tr>
    <th>
        @Html.DisplayNameFor(model => model.personaCedula)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaPasaporte)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaRuc)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaNombre)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaFechaNacimiento)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaSexo)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaEstadoCivil)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaNacionalidad)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaTelefonoMovil)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaCorreo)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.formaTratar)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaReferente)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.profesion)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.actividadEconomica)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.empresaTrabajo)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.tipoEmpresa)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.nombreComercial)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.paginaWeb)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.tipoIdRepresentante)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.identificacionRepresentante)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.nombreRepresentante)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaTipo)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.usuarioCreacion)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.fechaModificacion)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.horaModificacion)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.usuarioModificacion)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.fechaCreacion)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.horaCreacion)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.lugarNacimiento)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.progCreacion)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.esRif)
    </th>
    <th>
        @Html.DisplayNameFor(model => model.personaCategoria)
    </th>
    <th></th>
</tr>

@if (Model.Count() == 0)
{   <tr>
        <td colspan = "3" > No se encontraron resultados </td>
    </tr>
}
else
{

foreach (var item in Model)
{

    <tr>
        <td>
            @Html.DisplayFor(modelItem => item.personaCedula)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaPasaporte)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaRuc)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaNombre)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaFechaNacimiento)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaSexo)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaEstadoCivil)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaNacionalidad)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaTelefonoMovil)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaCorreo)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.formaTratar)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaReferente)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.profesion)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.actividadEconomica)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.empresaTrabajo)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.tipoEmpresa)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.nombreComercial)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.paginaWeb)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.tipoIdRepresentante)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.identificacionRepresentante)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.nombreRepresentante)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaTipo)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.usuarioCreacion)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.fechaModificacion)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.horaModificacion)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.usuarioModificacion)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.fechaCreacion)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.horaCreacion)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.lugarNacimiento)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.progCreacion)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.esRif)
        </td>
        <td>
            @Html.DisplayFor(modelItem => item.personaCategoria)
        </td>
        <td>
            @Html.ActionLink("Edit", "Edit", new { id = item.personaNumero }) |
            @Html.ActionLink("Details", "Details", new { id = item.personaNumero }) |
            @Html.ActionLink("Delete", "Delete", new { id = item.personaNumero })
        </td>
    </tr>
}

}