Dynamical model 1:
ARBOTHAI Dengue Forecasting Framework

Overview

The model is a discrete-time stochastic compartmental model describing dengue transmission with two viral strains, antibody-dependent enhancement (ADE), temporary cross-immunity, and asymptomatic infections.

The framework is designed for endemic settings such as Thailand, where multiple dengue serotypes co-circulate, secondary infections are more severe, and transmission is strongly seasonal and climate-sensitive. The model is intended to be integrated with mobility and climate data and used for simulation, inference, and scenario analysis.

Epidemiological Scope

Dengue transmission is characterised by complex immunological interactions between serotypes. Primary infection confers lifelong immunity to the infecting strain but only temporary cross-immunity to others. Subsequent infections can result in antibody-dependent enhancement, increasing both susceptibility and disease severity.

Many classical dengue models simplify these processes. This model explicitly represents:

• Primary and secondary infections
• Temporary cross-immunity
• Symptomatic and asymptomatic cases
• Enhanced severity and mortality during secondary infections
• Stochastic variability in transmission and progression

1. Model Structure

The model tracks transitions between compartments at each time step using probabilistic rules, typically sampled from binomial distributions, with transition probabilities derived from biological parameters (e.g., incubation rate, recovery rate) and the time-varying force of infection.he total human population \(N(t)\) is divided into the following compartments.

Primary infection states

$S_{\text{both}}$: Susceptible to both strains
$E_1, E_2$: Exposed (latent) to strain 1 or 2
$I_1, I_2$: Symptomatic primary infections
$A_1, A_2$: Asymptomatic primary infections

Cross-immunity and secondary infection states

$CI_1, CI_2$: Temporary cross-immunity after infection with strain 1 or 2
$S_1, S_2:$ Susceptible to strain 1 or 2 after immunity wanes
$E_{12}, E_{21}$: Secondary exposure (strain 1 after 2, or vice versa)
$I_{12}, I_{21}$: Symptomatic secondary infections (ADE)
$A_{12}, A_{21}$: Asymptomatic secondary infections (ADE)
Final states

$R$: Fully recovered and immune
$D$: Dengue-induced deaths

The total population is conserved except for disease-induced mortality:
$N = \sum_{i} X_i$
Force of Infection

Transmission from mosquitoes to humans is represented implicitly through strain-specific forces of infection:
$\lambda_1(t) = \beta_{mh,1}(t) \frac{I_1 + k_a A_1 + I_{12} + k_a A_{12}}{N}$

$\lambda_2(t) = \beta_{mh,2}(t) \frac{I_2 + k_a A_2 + I_{21} + k_a A_{21}}{N}$
where:

– ($\beta_{mh,i}(t)$) is the mosquito-to-human transmission rate for strain \(i\)
– ($k_a$) scales the infectiousness of asymptomatic infections

At its foundation, the model adopts a discrete-time stochastic compartmental approach. The human population is divided into a set of epidemiological states that account for infection with two distinct dengue virus strains, along with immunological responses such as temporary cross-immunity and antibody-dependent enhancement (ADE) during secondary infections. The compartments include:

Seasonal and Climate Forcing

Temporal variability in dengue transmission is treated in the model primarily as a climate-driven process, reflecting the strong empirical and mechanistic links between environmental conditions and mosquito-borne transmission. Simulated seasonality is included only as an alternative or baseline representation when explicit climate data are unavailable.

To encompass both approaches within a unified formulation, the mosquito-to-human transmission rate is written as:

where ($\beta_0$) is the baseline transmission intensity and ($f(t)$) is a non-negative, time-varying modulation function.

Climate-driven transmission

In the main modelling configuration, temporal changes in transmission are driven explicitly by climate variables. The modulation function depends on temperature and precipitation:

where (T(t)) and (P(t)) denote temperature and precipitation at time (t), respectively. The function (g(\cdot)) captures the combined effects of climate on mosquito abundance, survival, biting rates, and viral development within the vector. Its functional form is defined externally to the epidemiological model and may be nonlinear, threshold-based, or empirically calibrated.
This formulation allows the epidemiological model to be directly coupled to climate data, enabling attribution analyses, counterfactual climate scenarios, and climate-informed forecasting. Importantly, it allows transmission to respond dynamically to interannual climate variability rather than imposing a fixed seasonal pattern.

Simulated seasonality (feedback model)

When reliable climate data are not available, or for methodological comparison, transmission seasonality can be imposed synthetically using harmonic forcing:

where ($a_k$) are amplitudes, ($\phi_k$) phase shifts, and ($T$) the fundamental period (typically one year). This approach provides a flexible approximation of recurrent seasonal patterns but does not explicitly represent the underlying environmental drivers.

Within the overall modelling strategy, simulated seasonality is therefore treated as a secondary or baseline scenario, while climate-driven transmission constitutes the primary and preferred representation of temporal variability.

Role of Exogenous Variables

Climate variables and seasonal drivers enter the model exclusively through the time-varying transmission rate ($\beta_{mh}(t)$). These variables are treated as exogenous inputs, meaning that their dynamics are not influenced by the epidemiological state of the system.

Temperature, precipitation, or synthetic seasonal signals modulate transmission intensity by affecting mosquito-related processes such as abundance, survival, biting frequency, and viral development. However, the mosquito population itself is not modelled explicitly. Instead, its net effect is captured through ($\beta_{mh}(t)$).

This separation ensures a clear conceptual distinction between:

• Endogenous dynamics, driven by human infection history, immunity, and stochastic transmission; and
• Exogenous forcing, imposed by environmental variability or prescribed seasonality.

As a result, the model can be flexibly coupled to external climate datasets or scenario-based forcings without altering its internal epidemiological structure.

Fitting and Forecasting Approach

The model is calibrated individually for each province or locality using historical dengue surveillance data (typically from 2009-2023). Parameter estimation relies on fitting probabilistic distributions to weekly case data, adjusting for local transmission dynamics, seasonality, and environmental conditions.

Forecasts are generated for 3-, 6-, and 12-month horizons under three configurations:

• Short-term (3-6 months): Using best-fit parameter distributions and corrected initial conditions (y₀) from recent observed data.
• Long-term (12 months): Using fitted parameter distributions, but sampling y₀ probabilistically based on recent historical compartment estimates (e.g., average infected, recovered, etc.).

Model output includes expected incidence trajectories and uncertainty bounds derived from multiple stochastic realizations.

Regional Customization and Climate Integration

The model is customized per province, allowing each region to have distinct transmission dynamics (e.g., stronger or weaker seasonality). This localized approach increases realism and improves fit quality. Climate effects are incorporated through the integration of region-specific ERA5 datasets, including daily or weekly resolution of temperature and rainfall.

Operational Relevance

ARBOTHAI is designed to inform public health decisions by providing:

• Scenario-based simulations (e.g., high rainfall year vs. dry year),
• Early warning signals for outbreak onset and severity,
• Region-specific forecasts accounting for climatic and epidemiological variability.

Its reliance on routinely available climate data and moderate entomological inputs makes the model scalable and applicable in data-limited contexts, while its modular structure allows adaptation to evolving knowledge and surveillance infrastructure.

Strengths of the model

• Explicit representation of ADE and cross-immunity
• Stochastic formulation with integer populations
• Separation of symptomatic and asymptomatic infections
• Flexible seasonal and climate forcing

This model provides a biologically realistic and flexible framework for dengue transmission modelling in endemic settings. Its explicit treatment of immunity, ADE, and stochasticity makes it particularly well suited for integration with mobility and climate data, supporting both scientific analysis and policy-relevant decision-making.