Mechanistic (process-based) epidemiological models derived from the Ross–MacDonald framework form the backbone of vector-borne disease forecasting. These models explicitly encode biological and ecological processes and allow climatic drivers—particularly temperature (T) and precipitation (P)—to directly modulate transmission dynamics. By embedding climate-dependent functions into transmission, survival, and incubation processes, these models provide a principled framework for projecting epidemic risk under environmental variability.
🔬 1. Compartmental Structure and Flow
Climate-sensitive mechanistic models typically adopt SEIR-type compartmental structures and explicitly represent two interacting populations:
• Host population (e.g., humans), indexed by H
• Vector population (e.g., mosquitoes), indexed by V
Each population is divided into epidemiological compartments:
Susceptible (S): Vulnerable to infection
Exposed (E): Infected but not yet infectious
Infectious (I): Capable of transmitting infection
Recovered (R): Immune individuals (host population only)
A defining feature of these models is that transition rates are explicit functions of climate, primarily temperature, allowing environmental variability to directly influence epidemic timing and intensity.
📈 2. Mathematical Formulation
Vector-borne disease transmission is modeled using systems of Ordinary Differential Equations (ODEs). These equations track population flows between compartments and allow derivation of stability properties and the basic reproduction number R₀.
📐 2.1 Climate-Sensitive Biological Functions
Key vector traits are modeled as temperature-dependent functions:
Vector biting rate:
a(T)
Vector mortality rate:
μᵥ(T)
Extrinsic incubation progression rate:
σᵥ(T)
The Extrinsic Incubation Period (EIP) is the time required for pathogen development inside the vector. Its inverse, σᵥ(T), increases with temperature within viable biological limits and is a dominant determinant of epidemic potential.
📐 2.2 Coupled Host–Vector SEIR System
Let Nₕ denote the total host population and Nᵥ the total vector population.
Host population dynamics (Sₕ, Eₕ, Iₕ, Rₕ):
dSₕ / dt = Λₕ − [ a(T) · βₕ · Iᵥ / Nₕ ] · Sₕ − μₕ · Sₕ
dEₕ / dt = [ a(T) · βₕ · Iᵥ / Nₕ ] · Sₕ − ( σₕ + μₕ ) · Eₕ
dIₕ / dt = σₕ · Eₕ − ( γₕ + μₕ ) · Iₕ
dRₕ / dt = γₕ · Iₕ − μₕ · Rₕ
Vector population dynamics (Sᵥ, Eᵥ, Iᵥ):
dSᵥ / dt = Λᵥ − [ a(T) · βᵥ · Iₕ / Nₕ ] · Sᵥ − μᵥ(T) · Sᵥ
dEᵥ / dt = [ a(T) · βᵥ · Iₕ / Nₕ ] · Sᵥ − ( σᵥ(T) + μᵥ(T) ) · Eᵥ
dIᵥ / dt = σᵥ(T) · Eᵥ − μᵥ(T) · Iᵥ
Climate enters the system explicitly through:
a(T), μᵥ(T), and σᵥ(T)
📋 3. Parameter Definitions
| Parameter | Definition | Role in the Model |
|---|---|---|
| a(T) | Temperature-dependent vector biting rate | Controls host–vector contact frequency |
| βₕ | Transmission probability from vector to host | Governs host infection risk |
| βᵥ | Transmission probability from host to vector | Governs vector infection risk |
| μᵥ(T) | Temperature-dependent vector mortality rate | Regulates vector lifespan |
| σᵥ(T) | Temperature-dependent EIP progression rate | Controls onset of vector infectiousness |
| σₕ | Host incubation rate | Governs Eₕ → Iₕ transition |
| γₕ | Host recovery rate | Governs Iₕ → Rₕ transition |
| Λₕ, Λᵥ | Recruitment rates | Maintain host and vector population turnover |
The core measure of epidemic potential, the Basic Reproduction Number (R0), is proportional to functions incorporating the biting rate, EIP, and vector lifespan, demonstrating high sensitivity to temperature:
📊 4. Parameter Ranges for Viral Vector-Borne Diseases
| Parameter | Typical Range | Interpretation |
|---|---|---|
| Optimal temperature for transmission | 26 °C – 30 °C | Maximizes dengue, Zika, chikungunya transmission |
| Malaria temperature threshold | ≥ 18 °C | Minimum for Plasmodium development |
| Host recovery rate γₕ | 0.07 – 0.14 day⁻¹ | Infectious period of 7–14 days |
| Vector incubation period (EIP) | Decreases with T | Faster transmission at higher temperatures |
| Vector mortality μᵥ(T) | High outside optimum | Extreme heat (>35 °C) suppresses transmission |
| Precipitation P | Context-dependent | Influences breeding-site availability |
🌐 5. Applicability and Limitations
Applicability
• Climate-driven forecasting of vector-borne disease risk
• Seasonal and interannual epidemic anticipation
• Evaluation of vector-control interventions
• Projection of geographic expansion under climate change
Limitations
• Limited integration of socioeconomic and behavioral drivers
• Sparse empirical data for thermal response validation
• Homogeneous mixing assumptions within populations
• Sensitivity to uncertainty in climate–biology relationships
📚 References
1. Aron, J.L. and May, R.M. (1982) The population dynamics of malaria. In The Population Dynamics of Infectious Diseases: Theory and Applications.
2. Caminade, C. et al. (2014) Impact of climate change on global malaria distribution. Proc. Natl. Acad. Sci. U. S. A..
3. Liu-Helmersson, J. et al. (2014) Vectorial capacity of Aedes aegypti: effects of temperature and implications for global dengue epidemic potential. PLoS One.
4. Mordecai, E.A. et al. (2017) Detecting the impact of temperature on transmission of Zika, dengue, and chikungunya using mechanistic models. PLoS Negl. Trop. Dis..
5. Tjaden, N.B. et al. (2017) Modelling the effects of global climate change on chikungunya transmission in the 21st century. Sci. Rep..