Why is the human biting rate squared in the Ross–Macdonald formula?

The biting rate is squared because vector transmission requires two independent bites: one for the mosquito to acquire the pathogen from an infected human, and a second to transmit it to a susceptible human.

What is the difference between R0 and Vectorial Capacity (V)?

Vectorial capacity measures the daily transmission potential purely from vector-human interaction factors, whereas R0 incorporates pathogen-specific transmission efficiencies (b, c) and the human infectious duration (1/r).

What does the critical mosquito density indicate?

Critical mosquito density (m_c) represents the minimum female mosquito-to-human ratio required to maintain an endemic transmission state (R0 ≥ 1).

How are the parameter elasticities interpreted?

Elasticity measures proportional sensitivity: an elasticity of 2 for biting rate means a 10% decrease in biting rate produces approximately a 20% reduction in R0.

Can this tool be used for real-time outbreak forecasting?

No. This tool is designed strictly as an educational model to explore theoretical dynamics and parameter relationships, not as an operational forecasting system.

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Mosquito-borne Disease Basic Reproduction Number R0 Tutor

Ross–Macdonald R0 = m·a²·b·c·pⁿ/(−r·ln p) for malaria, dengue, Zika or chikungunya: herd-immunity threshold, vectorial capacity, critical mosquito density, parameter elasticities, control targets and a seasonal transmission-window curve.

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What this tool helps you do

A teaching tool for the basic reproduction number of mosquito-borne pathogens.

The Ross–Macdonald formula R0 = m·a²·b·c·pⁿ/(−r·ln p) is computed from: m = female mosquitoes per human, a = human biting rate (bites per mosquito per day — squared because each bite is a two-way journey), b = mosquito→human transmission probability, c = human→mosquito probability, p = daily mosquito survival, n = extrinsic incubation period (EIP, days the virus/parasite needs before the mosquito becomes infectious), r = human recovery rate.

Derived outputs: herd-immunity threshold 1−1/R0; Garrett-Jones vectorial capacity V = m·a²·pⁿ/(−ln p) with R0 = V·b·c/r; critical mosquito density m_c = m/R0; elasticity analysis (∂lnR0/∂lnθ) showing biting rate (×2) and adult survival (n + 1/(−ln p)) as the dominant levers; one-lever control targets — density, biting rate a/√R0 and the survival level (bisection) that bring R0 below 1; and a 365-day seasonal R0(t) curve with sinusoidal mosquito-density forcing showing when the transmission season opens and closes.

Presets: malaria (the classic worked example, R0 ≈ 74.5), dengue (WHO 8–12 day EIP, 4.5-day viremia), Zika and chikungunya, or fully custom parameters. Educational model — not an operational forecast.

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1. Textbook Malaria Dynamics and Sensitivity Analysis

2. Seasonal Dengue Transmission Window Estimation

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