Optimal control and cost-effectiveness analysis of a network-inspired multihost fascioliasis model

Fascioliasis is an environmentally mediated zoonotic disease sustained by nonlinear interactions among humans, livestock, freshwater snails, and contaminated aquatic environments. In endemic agricultural settings, transmission is influenced by heterogeneous contact structures arising from clustered village interactions, shared water sources, and livestock movement. A deterministic multihost transmission framework is formulated in which connectivity effects are incorporated through effective transmission coefficients derived from a mean-field approximation of contact structure. The model integrates human, cattle, snail, and environmental compartments within a system of ordinary differential equations, allowing representation of host-environment feedback mechanisms. Time dependent intervention strategies, including treatment, surveillance, and environmental management, are incorporated within an optimal control framework over a finite time horizon. The basic reproduction number is obtained using the next-generation matrix approach, and necessary optimality conditions are derived via Pontryagin's Maximum Principle. Numerical solutions are computed using a forward-backward sweep algorithm, and cost-effectiveness analysis is employed to compare intervention strategies. Results indicate that parameters associated with snail population dynamics and environmental contamination exert a dominant influence on transmission intensity. Combined intervention strategies achieve greater reductions in infection prevalence relative to single-control approaches under baseline parameter values. Several parameters are specified based on biologically plausible assumptions due to limited empirical data, and connectivity is represented through a mean-field approximation rather than an explicitly resolved contact network. Consequently, the findings provide qualitative insights into transmission dynamics and intervention design. The framework highlights the role of environmental persistence and structured contact patterns in sustaining fascioliasis transmission and supports the development of integrated control strategies in endemic regions.