How can I control this latch with Positive Logic?
To control the circuit with positive logic, replace each of the switches with a general purpose low power transistor like shown in the circuit below.







simulate this circuit &ndash; Schematic created using CircuitLab

If your input is fed from more than 5V power supply, you may consider increasing R1. Eg. 2k7 for 12V-15V.

The circuit may very well work with higher resistors, but you didn't spec any currents/resistors in yours so I have to be on the safe side.