Disable out of stock item (hide in categories, search results) - prestashop 1.6

Hi I wish to hide products in the front office that have available quantity = to zero. When I sell a product I do not wish to delete it from prestashop because I want to have sales statistics. But I do not want these products to show up in the front end at all. I wish to totaly hide these products. Can I do this with your module? 
Please clarify the following: If I sell a product then its quantity is zero. If I search for this product in the front office I do not want it to show up at all. So the customer will never be able to visit its product page. When does your module redirect to the home page? The product doesnt exist so the client will not be able to visit its product page to be redirected to the home page. I am understanding something wrong?
I am running PS 1.6.0.6.

Hi,
this can be done with "seo redirect" module from our offer. It has feature to "hide out of stock" products and redirect page of hidden product to other page (to avoid 404 errors - like it is by default when product is disabled). 

When someone will purchase an item and if quantity of this item is equal to 0 (or less) - module will perform a specific action that you can select on module configuration page:
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Nothing
Module will just do nothing ;-)

unassign from all categories and move to new category
For example you've got category "Archive" where you want to move all sold items. Product will be removed from all categories and then assigned to category can point during configuration

Assign to selected category
Module will assign product to selected category (so in effect product will be in all previous categories + in one new category)

Unassign from selected category
Module will unasing product from selected category

Disable & hide automatically
Product will be disabled and not available in your shop

Disable and redirect to shop homepage
Product will be disabled and customer redirected to homepage (when for example customer will search in google and click on link that will open product page)

disable and redirect to main category of product
Product will be disabled and customer that tries to open product page (for example from google) will be redirected to main category page of product

Disable visibility in shop's catalog
Product will not be disabled, but it will be not visible in products catalog (categories, search results) - product page will be still accessible (for example from google search results)

So,

depending on what your expactaction is - you can select one action. 
You mentioned that you want to hide product (both in catalog and product page) - so you just select "Disable and redirect to shop homepage" or "disable and redirect to main category of product"
(you will avoid 404 errors when product will be just disabled without any kind of redirection)

best regards
milos