How is immunity developed after a primary infection by bacteria?

Phagocytosis - A phagocyte detects the bacteria has foreign antigens and so envelops it with its cytoplasm, packaging it into a phagosome via endocytosis. Lysosomes then fuse with the phagosome releasing hydrolitic enzymes called lysozymes. These hydrolyse the bacteria and release its antigens so that they can fuse with the cell membrane of the phagocyte. The phagocyte is now antigen presentingT-helper cells with a complimentary receptor to the antigens of the pathogen are then activated and these find also complimentary B and T lymphocytes and activate them with cytokines. These B lymphocytes then undergo mitosis to produce B-plasma and B-memory cells. The T lymphocytes undergo mitosis to produce T-memory and T-killer cells. The respective memory cells are used in immunity for when there is a secondary infection, undergoing quick mitosis when the same foreign antigen is detected.