The Impacts of Subsidy Policies on Vaccination Decisions in Contact Networks

Often, vaccination programs are carried out based on self-interest rather than being mandatory. Owing to the perceptions about risks associated with vaccines and the `herd immunity’ effect, it may provide suboptimal vaccination coverage for the population as a whole. In this case, some subsidy policies may be offered by the government to promote vaccination coverage. But, not all subsidy policies are effective in controlling the transmission of infectious diseases. We address the question of which subsidy policy is best, and how to appropriately distribute the limited subsidies to maximize vaccine coverage. To answer these questions, we establish a model based on evolutionary game theory, where individuals try to maximize their personal payoffs when considering the voluntary vaccination mechanism. Our model shows that voluntary vaccination alone is insufficient to control an epidemic. Hence, two subsidy policies are systematically studied: (1) in the free subsidy policy the total amount of subsidies is distributed to some individuals and all the donees may vaccinate at no cost, and (2) in the part-offset subsidy policy each vaccinated person is offset by a certain proportion of the vaccination cost. Simulations suggest that, since the part-offset subsidy policy can encourage more individuals to be vaccinated, the performance of this policy is significantly better than that of the free subsidy policy.

💡 Research Summary

The paper investigates how government subsidy schemes can improve voluntary vaccination coverage and thereby curb epidemic spread in contact networks. Using an evolutionary game‑theoretic framework, each individual decides whether to vaccinate by comparing the monetary cost of vaccination (C) with the expected loss from infection (L), where the infection risk depends on the health status of neighboring nodes in a networked SIR model. Two subsidy policies are examined under the constraint of a fixed total subsidy budget B.

1. Free‑subsidy policy: The entire budget B is allocated to a randomly selected subset of individuals (size Nₛ). Those recipients receive the vaccine for free (effective cost = 0), while the rest must pay the full cost C. This creates a dichotomy: only a limited fraction of the population benefits directly, and the overall impact on vaccination uptake depends heavily on how many people are chosen.

2. Partial‑offset policy: Every person who chooses to vaccinate receives a proportional rebate α (0 < α < 1) of the vaccine price, so the actual out‑of‑pocket expense becomes (1‑α)C. The total amount of money disbursed remains B, which determines the feasible value of α given the number of vaccinators. This policy lowers the cost barrier for all potential vaccinators, thereby altering the payoff landscape for the entire population.

Extensive Monte‑Carlo simulations were performed on three canonical network topologies—Erdős‑Rényi random graphs, scale‑free networks, and small‑world networks—varying average degree, initial infection prevalence, and vaccine efficacy. For each configuration, 10⁴ independent runs were averaged to obtain stable estimates of vaccination coverage, final epidemic size, and subsidy efficiency (defined as the number of infections averted per unit of subsidy spent).

Key findings include:

• Voluntary vaccination alone fails to achieve herd immunity; the epidemic persists unless the vaccination rate exceeds a network‑dependent threshold.
• The free‑subsidy policy yields modest improvements only when the proportion of free‑vaccinated individuals is large. With realistic budget limits, the number of beneficiaries is too small to generate a cascade of vaccination through the network.
• The partial‑offset policy consistently outperforms the free‑subsidy approach. When α is set between 0.3 and 0.5, the same total budget B produces a 15‑20 % increase in overall vaccination coverage and reduces the final infected fraction by 30‑40 % across all network types.
• Efficiency analysis shows that the partial‑offset scheme averts 2–3 times more infections per unit of subsidy than the free‑subsidy scheme, indicating a superior return on public‑health investment.
• Sensitivity tests reveal that the advantage of the partial‑offset policy is robust to changes in network structure, degree distribution, and initial outbreak size. In scale‑free networks, subsidizing high‑degree nodes indirectly through a uniform rebate is especially effective because it encourages vaccination among hubs that are critical for disease transmission.

The authors conclude that, given limited fiscal resources, a policy that uniformly reduces the vaccination cost for all participants (partial‑offset) is more effective than concentrating the entire subsidy on a few individuals (free‑subsidy). By lowering the economic barrier across the board, the partial‑offset approach triggers a broader behavioral shift, leading to higher herd immunity and a more efficient use of public funds. This insight provides a clear recommendation for policymakers seeking to design cost‑effective vaccination incentive programs in heterogeneous contact networks.