In the controller, you can create a variable to determine if the form has been deleted:
app.controller('NameController', ['$scope', function($scope) {
$scope.submitted = false;
$scope.formProcess = function(form) {
$scope.submitted = true;
}
}]);
Than in your opinion:
<form ng-submit="formProcess(form)">
<p>
<label for="first_name">First Name</label>
<input type="text" name="first_name" id="first_name" ng-model="firstName" ng-pattern="/^[a-zA-Z\s]*$/" required/>
<span class="error" ng-if="submitted" && ng-messages="contact_form.first_name.$error">
<span ng-message="required">First name should not be empty</span>
<span ng-message="pattern" ng-show="contact_form.first_name.$error.pattern">Only alphabets allowed</span>
</span>
</p>
<p>
<button class="btn btn-secondary" type="submit">Send</button>
</p>
</form>