A theoretical model describing the electron transport in vertical conductivity quantum dot infrared photodetectors is presented. The carrier wave functions and energy levels were evaluated using the strain dependent eight-band kp Hamiltonian and used to calculate all intra- and interperiod transition rates due to interaction with phonons and electromagnetic radiation. The interaction with longitudinal acoustic phonons and electromagnetic radiation was treated perturbatively within the framework of Fermi's golden rule, while the interaction with longitudinal optical phonons was considered taking into account their strong coupling to electrons. A system of rate equations was then formed, from which the macroscopic device output parameters such as dark current and responsivity, as well as microscopic information about carrier distribution in quantum dots and continuum states, could be extracted. The model has been applied to simulate the dark current, as well as the midinfrared photoresponse in an experimentally realized device [Chen, J. Appl. Phys. 89, 4558 (2001)], and a good agreement with experiment has been obtained. Being free from any fitting or phenomenological parameters, the model should be a useful tool in the design and prediction of the characteristics of the existing or other types of quantum dot infrared photodetectors.