A Multi-Host Deterministic Model with Optimal Control Strategies for Marburg Virus Disease

Abstract

Marburg virus disease (MVD) is a zoonotic viral haemorrhagic fever that presents continuing challenges for outbreak prevention and control. This study develops a deterministic compartmental model to examine transmission among humans, bats and monkeys, together with the contribution of environmental viral contamination. The human population is represented by susceptible, exposed, infectious, quarantined and recovered compartments, while susceptible and infected classes are considered for the animal hosts. The model incorporates direct and indirect transmission, quarantine, recovery, loss of immunity, and environmental viral shedding and decay. Non-negativity, boundedness, equilibria and reproduction-number thresholds are analysed. Latin hypercube sampling and sensitivity indices are used to examine parameter effects, while an optimal-control formulation evaluates quarantine and environmental interventions alongside behavioural responses. Under the assumed baseline parameters, model simulations indicate that environment-to-human exposure accounts for at least 99.3% of the human force of infection over the 50-day period. Environmental controls alone reduce the simulated infectious peak from 6.03 to 1.15 and the cumulative infectious burden by 85%. The combined intervention scenario produces the lowest reported objective value, although its infection trajectory is similar to that of environmental control alone. Increasing quarantine rates reduces simulated infectious peaks, whereas social distancing has limited influence in the environmentally dominated baseline scenario. These results underscore the importance of assessing multiple transmission routes when selecting interventions, while recognising that the findings depend on model structure and assumed parameter values.