Application of mathematical modelling to inform national malaria intervention planning in Nigeria

BACKGROUND

For their 2021-2025 National Malaria Strategic Plan (NMSP), Nigeria's National Malaria Elimination Programme (NMEP), in partnership with the World Health Organization (WHO), developed a targeted approach to intervention deployment at the local government area (LGA) level as part of the High Burden to High Impact response. Mathematical models of malaria transmission were used to predict the impact of proposed intervention strategies on malaria burden.

METHODS

An agent-based model of Plasmodium falciparum transmission was used to simulate malaria morbidity and mortality in Nigeria's 774 LGAs under four possible intervention strategies from 2020 to 2030. The scenarios represented the previously implemented plan (business-as-usual), the NMSP at an 80% or higher coverage level and two prioritized plans according to the resources available to Nigeria. LGAs were clustered into 22 epidemiological archetypes using monthly rainfall, temperature suitability index, vector abundance, pre-2010 parasite prevalence, and pre-2010 vector control coverage. Routine incidence data were used to parameterize seasonality in each archetype. Each LGA's baseline malaria transmission intensity was calibrated to parasite prevalence in children under the age of five years measured in the 2010 Malaria Indicator Survey (MIS). Intervention coverage in the 2010-2019 period was obtained from the Demographic and Health Survey, MIS, the NMEP, and post-campaign surveys.

RESULTS

Pursuing a business-as-usual strategy was projected to result in a 5% and 9% increase in malaria incidence in 2025 and 2030 compared with 2020, while deaths were projected to remain unchanged by 2030. The greatest intervention impact was associated with the NMSP scenario with 80% or greater coverage of standard interventions coupled with intermittent preventive treatment in infants and extension of seasonal malaria chemoprevention (SMC) to 404 LGAs, compared to 80 LGAs in 2019. The budget-prioritized scenario with SMC expansion to 310 LGAs, high bed net coverage with new formulations, and increase in effective case management rate at the same pace as historical levels was adopted as an adequate alternative for the resources available.

CONCLUSIONS

Dynamical models can be applied for relative assessment of the impact of intervention scenarios but improved subnational data collection systems are required to allow increased confidence in predictions at sub-national level.

A validated mathematical model of FGFR3-mediated tumor growth reveals pathways to harness the benefits of combination targeted therapy and immunotherapy in bladder cancer

Bladder cancer is a common malignancy with over 80,000 estimated new cases and nearly 18,000 deaths per year in the United States alone. Therapeutic options for metastatic bladder cancer had not evolved much for nearly four decades, until recently, when five immune checkpoint inhibitors were approved by the U.S. Food and Drug Administration (FDA). Despite the activity of these drugs in some patients, the objective response rate for each is less than 25%. At the same time, fibroblast growth factor receptors (FGFRs) have been attractive drug targets for a variety of cancers, and in 2019 the FDA approved the first therapy targeted against FGFR3 for bladder cancer. Given the excitement around these new receptor tyrosine kinase and immune checkpoint targeted strategies, and the challenges they each may face on their own, emerging data suggest that combining these treatment options could lead to improved therapeutic outcomes. In this paper, we develop a mathematical model for FGFR3-mediated tumor growth and use it to investigate the impact of the combined administration of a small molecule inhibitor of FGFR3 and a monoclonal antibody against the PD-1/PD-L1 immune checkpoint. The model is carefully calibrated and validated with experimental data before survival benefits, and dosing schedules are explored. Predictions of the model suggest that FGFR3 mutation reduces the effectiveness of anti-PD-L1 therapy, that there are regions of parameter space where each monotherapy can outperform the other, and that pretreatment with anti-PD-L1 therapy always results in greater tumor reduction even when anti-FGFR3 therapy is the more effective monotherapy.

Weather-driven malaria transmission model with gonotrophic and sporogonic cycles

Malaria is mainly a tropical disease and its transmission cycle is heavily influenced by environment: The life-cycles of the Anopheles mosquito vector and Plasmodium parasite are both strongly affected by ambient temperature, while suitable aquatic habitat is necessary for immature mosquito development. Therefore, how global warming may affect malaria burden is an active question, and we develop a new ordinary differential equations-based malaria transmission model that explicitly considers the temperature-dependent Anopheles gonotrophic and Plasmodium sporogonic cycles. Mosquito dynamics are coupled to infection among a human population with symptomatic and asymptomatic disease carriers, as well as temporary immunity. We also explore the effect of incorporating diurnal temperature variations upon transmission. Rigorous analysis of the model show that the non-trivial disease-free equilibrium is locally-asymptotically stable when the associated reproduction number is less than unity (this equilibrium is globally-asymptotically for a special case with no density-dependent larval and disease-induced host mortality). Numerical simulations of the model, for the case where the ambient temperature is held constant, suggest a nonlinear, hyperbolic relationship between the reproduction number and clinical malaria burden. Moreover, malaria burden peaks at 29.5 o C when daily ambient temperature is held constant, but this peak decreases with increasing daily temperature variation, to about 23-25 o C. Malaria burden also varies nonlinearly with temperature, such that small temperature changes influent disease mainly at marginal temperatures, suggesting that in areas where malaria is highly endemic, any response to global warming may be highly nonlinear and most typically minimal, while in areas of more marginal malaria potential (such as the East African highlands), increasing temperatures may translate nearly linearly into increased disease potential. Finally, we observe that while explicitly modelling the stages of the Plasmodium sporogonic cycle is essential, explicitly including the stages of the Anopheles gonotrophic cycle is of minimal importance.

Mathematical analysis of a weather-driven model for the population ecology of mosquitoes

A new deterministic model for the population biology of immature and mature mosquitoes is designed and used to assess the impact of temperature and rainfall on the abundance of mosquitoes in a community. The trivial equilibrium of the model is globally-asymptotically stable when the associated vectorial reproduction number (R0) is less than unity. In the absence of density-dependence mortality in the larval stage, the autonomous version of the model has a unique and globally-asymptotically stable non-trivial equilibrium whenever 1 andlt;R0 andlt;RC0 (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at R0=RC0). Numerical simulations of the weather-driven model, using temperature and rainfall data from three cities in Sub-Saharan Africa (Kwazulu Natal, South Africa; Lagos, Nigeria; and Nairobi, Kenya), show peak mosquito abundance occurring in the cities when the mean monthly temperature and rainfall values lie in the ranges [22-25]0C, [98-121] mm; [24-27]0C, [113-255] mm and [20.5-21.5]0C, [70-120] mm, respectively (thus, mosquito control efforts should be intensified in these cities during the periods when the respective suitable weather ranges are recorded).

Mathematical analysis of a model for zoonotic visceral leishmaniasis

Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many parts of the world (notably in Africa, Asia and the Mediterranean). This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations. The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models. In the absence of such phenomenon (which is shown to arise due to the disease-induced mortality in the host populations), the nontrivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality of Brazil, it is shown, for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts, that the associated reproduction number of the model ( ℛ 0 ) ranges from 0.3 to 1.4, with a mean of ℛ 0 = 0.85 . Furthermore, when the effect of such drug treatment is explicitly incorporated in the model (i.e., accounting for the additional larval and sandfly mortality, following feeding on the treated reservoirs), the range of ℛ 0 decreases to ℛ 0 ∈ [ 0.1 , 0.6 ] , with a mean of ℛ 0 = 0.35 (this significantly increases the prospect of the effective control or elimination of the disease). Thus, ZVL transmission models (in communities where such treatment strategy is implemented) that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of ℛ 0 ) in the community. It is shown that ℛ 0 is more sensitive to increases in sandfly lifespan than that of the animal reservoir (so, a strategy that focuses on reducing sandflies, rather than the animal reservoir (e.g., via culling), may be more effective in reducing ZVL burden in the community). Further sensitivity analysis of the model ranks the sandfly removal rate (by natural death or by feeding from insecticide-treated reservoir hosts), the biting rate of sandflies on the reservoir hosts and the progression rate of exposed reservoirs to active ZVL as the three parameters with the most effect on the disease dynamics or burden (as measured in terms of the reproduction number ℛ 0 ). Hence, this study identifies the key parameters that play a key role on the disease dynamics, and thereby contributing in the design of effective control strategies (that target the identified parameters).