You can supply settings to JsonConvert.DeserializeObject to tell it how to handle null values, in this case, and much more:
var settings = new JsonSerializerSettings
{
NullValueHandling = NullValueHandling.Ignore,
MissingMemberHandling = MissingMemberHandling.Ignore
};
var jsonModel = JsonConvert.DeserializeObject<Customer>(jsonString, settings);