Sensitivity Analysis and Optimal Control for Nipah Virus Outbreak

Abstrak

Nipah virus (NiV) is a zoonotic pathogen capable of causing outbreaks with high mortality rates, ranging from 40% to 75%. The virus spreads through direct contact between humans and infected animals, consumption of contaminated food, and human-to-human transmission. As no vaccine or specific treatment is currently available, effective control measures must rely on public health policies. In this study, we develop a mathematical model to examine the transmission dynamics of the Nipah virus. We calculate the basic reproduction number R0 as an indicator of disease spread, perform a sensitivity analysis of key model parameters, and evaluate the effectiveness of three control strategies: health campaigns targeting exposed individuals, quarantine of infected individuals, and treatment to increase the recovery rate. The objective is to minimize both the number of exposed and infected individuals and the overall cost of implementing these controls. The model used is a compartmental framework dividing the human population into five subgroups: susceptible (S), exposed (E), infected (I), recovered (R), and deceased (D). To identify the optimal intervention strategy, we apply the Pontryagin Maximum Principle (PMP), and the resulting optimality system is solved numerically using the Forward–Backward Sweep method. The results show that the effective contact rate, incubation period, and treatment rate are the most influential parameters in determining disease transmission. Sensitivity analysis indicates that reducing R0 is most effectively achieved by improving the efficiency of health campaigns and treatment. Numerical simulations further demonstrate that the optimal combination of all three control strategies significantly reduces both exposed and infected populations compared with implementing any single strategy alone. With an optimally designed set of interventions, the resulting policy achieves a balance between controlling viral spread and ensuring cost efficiency.