DELENDA demonstrates an uncertainty-first approach to subnational tailoring: differentiable model structure exposes the biological parameter space to posterior calibration and carries biological and operational uncertainty into constrained decision optimization, tasks that are difficult with the non-differentiable models currently central to SNT workflows.
Abstract
Malaria subnational tailoring is often a population-level allocation problem: which interventions should be prioritized, at what coverage, and under what budget and uncertainty assumptions? We present DELENDA, a differentiable compartmental model of Plasmodium falciparum transmission designed for posterior calibration and intervention-mix optimization. We fit a NUTS posterior jointly to age-stratified prevalence and clinical-incidence data from five sub-Saharan African sites plus three pre-intervention Garki Project villages, spanning a broad entomological inoculation rate (EIR) range. DELENDA is implemented in JAX, which makes the full simulation differentiable. This enables efficient Bayesian inference and continuous constrained optimization over intervention coverage. We apply the framework to an illustrative decision problem: a highly seasonal transmission setting where coverage is optimized for ITNs, SMC, IRS, and pediatric malaria vaccination across EIR, budget, objective, and uncertainty grids. Three findings are decision-relevant. First, intervention rankings are more robust than projected impact: posterior, vector-biology, and intervention-efficacy uncertainty change optimized coverage modestly but substantially widen the distribution of cases averted. Second, the objective matters: under-five optimization brings child-targeted SMC and vaccination in earlier, whereas all-age optimization delays vaccination and favors broader population protection through IRS. Third, cost uncertainty is mainly a constraint-side problem: expected-cost optima have material budget-overrun probability, while tail-risk budget rules sharply reduce overrun risk at the cost of lower effective coverage and fewer expected cases averted. DELENDA therefore demonstrates an uncertainty-first approach to subnational tailoring: differentiable model structure exposes the biological parameter space to posterior calibration and carries biological and operational uncertainty into constrained decision optimization, tasks that are difficult with the non-differentiable models currently central to SNT workflows.
Models incorporating household structure, with different rates of transmission within and between households, are widely used in infectious disease epidemiology. These models can be calibrated using final-size data in which transmission ordering is ignored because it does not affect the distribution of final outbreak sizes. In particular, many distinct transmission histories produce identical final epidemiological outcomes, making it difficult to distinguish internal (within-household) from external (between-household) transmission and limiting parameter identifiability. Here, we develop a continuous-time Markov chain formulation for household transmission dynamics in which the model state space is expanded to include transmission graphs describing infection direction and order, with idealised pathogen genomic data used to identify the transmission histories compatible with observations. We conduct simulation studies which show that incorporating genetic information substantially concentrates the regions of high likelihood compared with models based on epidemiological data alone. In particular, genomic data reduces the dependence between internal and external transmission parameters, removing the characteristic ridge associated with their weak identifiability. These results demonstrate that graph-resolved household models enable improved transmission inference while maintaining analytical and computational tractability.
Modern Bayesian hierarchical methodologies allow us to leverage spatio-temporal dependencies between observations, enhancing both health effect estimation and map visualization in efficient and flexible ways. However, the necessary levels of statistical software are often unavailable or difficult to access. We have recently examined Bayesian spatio-temporal models to estimate the association between COVID-19 death counts and various social and environmental risk factors, including ambient air pollution exposure. Typically, it is very common that in an infection disease mapping problem with count data, we have excessive zeros, and it is usually for over-dispersed count outcome variables. Furthermore, the theory suggests that the excess zeros are generated by a separate process from the count values and that the excess zeros need to be modeled independently. Our proposed models are specially designed to handle the zero-inflation and over-dispersion in count data through Zero-Inflated Negative Binomial regression with random effects that vary across time and space within a Markov Chain Monte Carlo framework. Drawing on our knowledge and experience, we aim to provide a simple, unified, and publicly available software that can be applied in various disease mapping studies under the contemporary Bayesian framework.
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