<p>This paper investigates the manner in which trust develops progressively and changes over time among networked entities through opinions, negative or positive, that these entities express about each other. The entities receive “voting rights” from an external regulator, and these rights are depleted as each entity expresses its opinions about other entities. Also, entities that express their opinions frequently progressively lose their rights to “vote” about others, and the trust level also drops as entities receive “negative votes” from others, so that entities whose own trust level is at zero are unable to vote. The resulting model is named the Random Neural Network Trust Model (RNNTM), and is an instance of the Random Neural Network. It is amenable to a compact and easily computable analytical solution which is presented, discussed and used in this paper. The use of the RNNTM is illustrated through time-dependent numerical simulations to represent trust among a set of entities that are affected by cyberattacks and by randomly lost messages, both with simulated input data and with real cyberattack sequences.</p>