Fish-borne Zoonotic Trematodes (FZTs) are a risk to human health and need to be controlled. A mathematical model was developed to give insight into how and to what extent control strategies change the dynamics of FZTs on integrated agriculture–aquaculture farms. The reproduction ratio R evaluates the effects of control strategies. R > 1 implies that the infection may persist, whereas R < 1 implies that the infection certainly cannot persist. In the absence of control strategies (default), R = 1.92. After implementing control strategies either (i) R and percentages infected hosts in the equilibrium did not change and FZTs persisted (ii) R became smaller, but not below 1, the new equilibrium had lower proportions of infected hosts, and FZTs persisted, or (iii) R became smaller than 1, and all hosts were FZT-free in the new equilibrium. Single chemotherapy of humans, reservoir hosts or both did not change R. Continuous chemotherapeutic treatment reduced R but not below 1 when treating only humans (R = 1.30) or only reservoir hosts (R = 1.69). A combination could result in R < 1, e.g. treating all humans and > 54% of reservoir hosts. Snail control could result in R < 1 with a decrease in density or increase in mortality of snails. This will occur when either transmission to snails or to fish is < 14% of its default value. Stocking fish at > 25 g as compared to 0.5 g that is usual in aquaculture practice, or at > 14 g in combination with treating all humans, led to R < 1. Advantage of using R for evaluating control strategies is that it provides insight into control success or failure even if it would take several decennia to observe this effect in the field.