A pathogen circulating in a wildlife reservoir (bats, rodents) occasionally spills over into humans through contact (hunting, farming, habitat loss). Once in humans, it may or may not sustain further human-to-human chains.
Spillover force of infection: λ = contact_rate × reservoir_prevalence
Human SIR: dS/dt=-βSI/N dI/dt=βSI/N-γI dR/dt=γI
Effective reproduction: R_eff = R₀ × (S/N)
- Reservoir prevalence — fraction of the wildlife reservoir currently infected (orange dots); the raw material for every spillover attempt.
- Contact rate — how often humans and reservoir animals interact (deforestation, live-animal markets, bushmeat); scales spillover attempt frequency.
- Human R₀ — average secondary human cases per human case if everyone were susceptible; below 1 an ignited chain fizzles out, above 1 it can grow into an epidemic.
- Recovery rate γ — inverse of the average infectious period; higher γ means people clear the infection faster.
Real-world relevance: this two-stage logic — reservoir spillover risk, then human R₀ — is exactly how epidemiologists assessed Ebola, SARS-CoV-2, Nipah and avian influenza during emergence, deciding whether a jump would stay a spillover or ignite a pandemic.