The role of mathematical modelling in guiding the science and economics of malaria elimination

Challenges of using modelling evidence in the visceral leishmaniasis elimination programme in India

As India comes closer to the elimination of visceral leishmaniasis (VL) as a public health problem, surveillance efforts and elimination targets must be continuously revised and strengthened. Mathematical modelling is a compelling research discipline for informing policy and programme design in its capacity to project incidence across space and time, the likelihood of achieving benchmarks, and the impact of different interventions. To gauge the extent to which modelling informs policy in India, this qualitative analysis explores how and whether policy makers understand, value, and reference recently produced VL modelling research. Sixteen semi-structured interviews were carried out with both users- and producers- of VL modelling research, guided by a knowledge utilisation framework grounded in knowledge translation theory. Participants reported that barriers to knowledge utilisation include 1) scepticism that models accurately reflect transmission dynamics, 2) failure of modellers to apply their analyses to specific programme operations, and 3) lack of accountability in the process of translating knowledge to policy. Political trust and support are needed to translate knowledge into programme activities, and employment of a communication intermediary may be a necessary approach to improve this process.

Modelling the Transmission Dynamics of COVID-19 in Six High-Burden Countries

The new Coronavirus Disease 19, officially known as COVID-19, originated in China in 2019 and has since spread worldwide. We presented an age-structured Susceptible-Latent-Mild-Critical-Removed (SLMCR) compartmental model of COVID-19 disease transmission with nonlinear incidence during the pandemic period. We provided the model calibration to estimate parameters with day-wise COVID-19 data, i.e., reported cases by worldometer from 15^th February to 30^th March 2020 in six high-burden countries, including Australia, Italy, Spain, the USA, the UK, and Canada. We estimate transmission rates for each country and found that the country with the highest transmission rate is Spain, which may increase the new cases and deaths than the other countries. We found that saturation infection negatively impacted the dynamics of COVID-19 cases in all the six high-burden countries. The study used a sensitivity analysis to identify the most critical parameters through the partial rank correlation coefficient method. We found that the transmission rate of COVID-19 had the most significant influence on prevalence. The prediction of new cases in COVID-19 until 30^th April 2020 using the developed model was also provided with recommendations to control strategies of COVID-19. We also found that adults are more susceptible to infection than both children and older people in all six countries. However, in Italy, Spain, the UK, and Canada, older people show more susceptibility to infection than children, opposite to the case in Australia and the USA. The information generated from this study would be helpful to the decision-makers of various organisations across the world, including the Ministry of Health in Australia, Italy, Spain, the USA, the UK, and Canada, to control COVID-19.

Scenario analysis for programmatic tuberculosis control in Bangladesh: a mathematical modelling study

Tuberculosis (TB) is a major public health problem in Bangladesh. Although the National TB control program of Bangladesh is implementing a comprehensive expansion of TB control strategies, logistical challenges exist, and there is significant uncertainty concerning the disease burden. Mathematical modelling of TB is considered one of the most effective ways to understand the dynamics of infection transmission and allows quantification of parameters in different settings, including Bangladesh. In this study, we present a two-strain mathematical modelling framework to explore the dynamics of drug-susceptible (DS) and multidrug-resistant (MDR) TB in Bangladesh. We calibrated the model using DS and MDR-TB annual incidence data from Bangladesh from years 2001 to 2015. Further, we performed a sensitivity analysis of the model parameters and found that the contact rate of both strains had the largest influence on the basic reproduction numbers [Formula: see text] and [Formula: see text] of DS and MDR-TB, respectively. Increasingly powerful intervention strategies were developed, with realistic impact and coverage determined with the help of local staff. We simulated for the period from 2020 to 2035. Here, we projected the DS and MDR-TB burden (as measured by the number of incident cases and mortality) under a range of intervention scenarios to determine which of these scenario is the most effective at reducing burden. Of the single-intervention strategies, enhanced case detection is the most effective and prompt in reducing DS and MDR-TB incidence and mortality in Bangladesh and that with GeneXpert testing was also highly effective in decreasing the burden of MDR-TB. Our findings also suggest combining additional interventions simultaneously leads to greater effectiveness, particularly for MDR-TB, which we estimate requires a modest investment to substantially reduce, whereas DS-TB requires a strong sustained investment.

Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh

Tuberculosis (TB) is the seventh leading cause of morbidity and mortality in Bangladesh. Although the National TB control program (NTP) of Bangladesh is implementing its nationwide TB control strategies, more specific and effective single or combination interventions are needed to control drug-susceptible (DS) and multi-drug resistant (MDR) TB. In this study, we developed a two strain TB mathematical model with amplification and fit it to the Bangladesh TB data to understand the transmission dynamics of DS and MDR TB. Sensitivity analysis was used to identify important parameters. We evaluated the cost-effectiveness of varying combinations of four basic control strategies including distancing, latent case finding, case holding and active case finding, all within the optimal control framework. From our fitting, the model with different transmission rates between DS and MDR TB best captured the Bangladesh TB reported case counts. The estimated basic reproduction number for DS TB was 1.14 and for MDR TB was 0.54, with an amplification rate of 0.011 per year. The sensitivity analysis also indicated that the transmission rates for both DS and MDR TB had the largest influence on prevalence. To reduce the burden of TB (both DS and MDR), our finding suggested that a quadruple control strategy that combines distancing control, latent case finding, case holding and active case finding is the most cost-effective. Alternative strategies can be adopted to curb TB depending on availability of resources and policy makers’ decisions.

Applied mathematical modelling to inform national malaria policies, strategies and operations in Tanzania

BACKGROUND

More than ever, it is crucial to make the best use of existing country data, and analytical tools for developing malaria control strategies as the heterogeneity in malaria risk within countries is increasing, and the available malaria control tools are expanding while large funding gaps exist. Global and local policymakers, as well as funders, increasingly recognize the value of mathematical modelling as a strategic tool to support decision making. This case study article describes the long-term use of modelling in close collaboration with the National Malaria Control Programme (NMCP) in Tanzania, the challenges encountered and lessons learned.

CASE DESCRIPTION

In Tanzania, a recent rebound in prevalence led to the revision of the national malaria strategic plan with interventions targeted to the malaria risk at the sub-regional level. As part of the revision, a mathematical malaria modelling framework for setting specific predictions was developed and used between 2016 and 2019 to (1) reproduce setting specific historical malaria trends, and (2) to simulate in silico the impact of future interventions. Throughout the project, multiple stakeholder workshops were attended and the use of mathematical modelling interactively discussed.

EVALUATION

In Tanzania, the model application created an interdisciplinary and multisectoral dialogue platform between modellers, NMCP and partners and contributed to the revision of the national malaria strategic plan by simulating strategies suggested by the NMCP. The uptake of the modelling outputs and sustained interest by the NMCP were critically associated with following factors: (1) effective sensitization to the NMCP, (2) regular and intense communication, (3) invitation for the modellers to participate in the strategic plan process, and (4) model application tailored to the local context.

CONCLUSION

Empirical data analysis and its use for strategic thinking remain the cornerstone for evidence-based decision-making. Mathematical impact modelling can support the process both by unifying all stakeholders in one strategic process and by adding new key evidence required for optimized decision-making. However, without a long-standing partnership, it will be much more challenging to sensibilize programmes to the usefulness and sustained use of modelling and local resources within the programme or collaborating research institutions need to be mobilized.

Life-table studies revealed significant effects of deforestation on the development and survivorship of Anopheles minimus larvae

BACKGROUND

Many developing countries are experiencing rapid ecological changes such as deforestation and shifting agricultural practices. These environmental changes may have an important consequence on malaria due to their impact on vector survival and reproduction. Despite intensive deforestation and malaria transmission in the China-Myanmar border area, the impact of deforestation on malaria vectors in the border area is unknown.

METHODS

We conducted life table studies on Anopheles minimus larvae to determine the pupation rate and development time in microcosms under deforested, banana plantation, and forested environments.

RESULTS

The pupation rate of An. minimus was 3.8 % in the forested environment. It was significantly increased to 12.5 % in banana plantations and to 52.5 % in the deforested area. Deforestation reduced larval-to-pupal development time by 1.9-3.3 days. Food supplementation to aquatic habitats in forested environments and banana plantations significantly increased larval survival rate to a similar level as in the deforested environment.

CONCLUSION

Deforestation enhanced the survival and development of An. minimus larvae, a major malaria vector in the China-Myanmar border area. Experimental determination of the life table parameters on mosquito larvae under a variety of environmental conditions is valuable to model malaria transmission dynamics and impact by climate and environmental changes.

Effect of Test-Based versus Presumptive Treatment of Malaria in Under-Five Children in Rural Ghana--A Cluster-Randomised Trial

BACKGROUND

Malaria-endemic countries in sub-Saharan Africa are shifting from the presumptive approach that is based on clinical judgement (CJ) to the test-based approach that is based on confirmation through test with rapid diagnostic tests (RDT). It has been suggested that the loss of the prophylactic effect of presumptive-administered ACT in children who do not have malaria will result in increase in their risk of malaria and anaemia.

METHODS AND FINDINGS

We undertook a cluster-randomized controlled trial to compare the effects of the presumptive approach using clinical judgment (CJ-arm) and the test-based approach using RDTs (RDT-arm in a high-transmission setting in Ghana. A total of 3046 eligible children (1527 in the RDT arm and 1519 in the CJ- arm) living around 32 health centres were enrolled. Nearly half were female (48.7%) and 47.8% were below the age of 12 months as at enrolment. Over 24-months, the incidence of all episodes of malaria following the first febrile illness was 0.64 (95% CI 0.49-0.82) and 0.76 (0.63-0.93) per child per year in the RDT and CJ arms respectively (adjusted rate ratio 1.13 (0.82-1.55). After the first episode of febrile illness, the incidence of severe anaemia was the same in both arms (0.11 per child per year) and that of moderate anaemia was 0.16 (0.13-0.21) vs. 0.17 (0.14-0.21) per child year respectively. The incidence of severe febrile illness was 0.15 (0.09, 0.24) in the RDT arm compared to 0.17 (0.11, 0.28) per child per year respectively. The proportion of fever cases receiving ACT was lower in the RDT arm (72% vs 81%; p = 0.02).

CONCLUSION

The test-based approach to the management of malaria did not increase the incidence of malaria or anaemia among under-five children in this setting.

TRIAL REGISTRATION

ClinicalTrials.gov NCT00832754.

Spatial heterogeneity, host movement and mosquito-borne disease transmission

Mosquito-borne diseases are a global health priority disproportionately affecting low-income populations in tropical and sub-tropical countries. These pathogens live in mosquitoes and hosts that interact in spatially heterogeneous environments where hosts move between regions of varying transmission intensity. Although there is increasing interest in the implications of spatial processes for mosquito-borne disease dynamics, most of our understanding derives from models that assume spatially homogeneous transmission. Spatial variation in contact rates can influence transmission and the risk of epidemics, yet the interaction between spatial heterogeneity and movement of hosts remains relatively unexplored. Here we explore, analytically and through numerical simulations, how human mobility connects spatially heterogeneous mosquito populations, thereby influencing disease persistence (determined by the basic reproduction number R0), prevalence and their relationship. We show that, when local transmission rates are highly heterogeneous, R0 declines asymptotically as human mobility increases, but infection prevalence peaks at low to intermediate rates of movement and decreases asymptotically after this peak. Movement can reduce heterogeneity in exposure to mosquito biting. As a result, if biting intensity is high but uneven, infection prevalence increases with mobility despite reductions in R0. This increase in prevalence decreases with further increase in mobility because individuals do not spend enough time in high transmission patches, hence decreasing the number of new infections and overall prevalence. These results provide a better basis for understanding the interplay between spatial transmission heterogeneity and human mobility, and their combined influence on prevalence and R0.

A mathematical model for the deficiency-excess mechanism of yin-yang in five viscera

To raise traditional medicine to a higher level of scientific research, a mathematical model has been proposed using symbolic notations and operators to describe several disease symptoms generally recognized in traditional medicine. Even though this model to a certain degree offers a mathematical approach to identify the relationships between yin-yang and the five viscera, it is not an efficient means of explaining the pathology in traditional medicine due to its use of superfluous notations and definitions. In this paper, we introduce two concise operators, a self-development operator and an action operator: the former describes the effect of a viscus in the unbalanced state on other viscera: the latter explains the engendering and restraining relationships between the two viscera. These tools are useful to elucidate the interactions among the states of the five viscera based on yin-yang and the five elements theory. Our mathematical model with these two operators facilitates description for the scheme of deficiency-excess of yin-yang in the five viscera. Accordingly, we have mathematically refined the existing results and shown clinical applications as well.

Optimising strategies for Plasmodium falciparum malaria elimination in Cambodia: primaquine, mass drug administration and artemisinin resistance

BACKGROUND

Malaria elimination requires a variety of approaches individually optimized for different transmission settings. A recent field study in an area of low seasonal transmission in South West Cambodia demonstrated dramatic reductions in malaria parasite prevalence following both mass drug administration (MDA) and high treatment coverage of symptomatic patients with artemisinin-piperaquine plus primaquine. This study employed multiple combined strategies and it was unclear what contribution each made to the reductions in malaria.

METHOD AND FINDINGS

A mathematical model fitted to the trial results was used to assess the effects of the various components of these interventions, design optimal elimination strategies, and explore their interactions with artemisinin resistance, which has recently been discovered in Western Cambodia. The modelling indicated that most of the initial reduction of P. falciparum malaria resulted from MDA with artemisinin-piperaquine. The subsequent continued decline and near elimination resulted mainly from high coverage with artemisinin-piperaquine treatment. Both these strategies were more effective with the addition of primaquine. MDA with artemisinin combination therapy (ACT) increased the proportion of artemisinin resistant infections, although much less than treatment of symptomatic cases with ACT, and this increase was slowed by adding primaquine. Artemisinin resistance reduced the effectiveness of interventions using ACT when the prevalence of resistance was very high. The main results were robust to assumptions about primaquine action, and immunity.

CONCLUSIONS

The key messages of these modelling results for policy makers were: high coverage with ACT treatment can produce a long-term reduction in malaria whereas the impact of MDA is generally only short-term; primaquine enhances the effect of ACT in eliminating malaria and reduces the increase in proportion of artemisinin resistant infections; parasite prevalence is a better surveillance measure for elimination programmes than numbers of symptomatic cases; combinations of interventions are most effective and sustained efforts are crucial for successful elimination.

Modelling malaria elimination on the internet

BACKGROUND

Unprecedented efforts are underway to eliminate malaria. Mathematical modelling can help to determine the optimal strategies for malaria elimination in different epidemiological settings. This is necessary as there is limited scope for expensive and time-consuming field studies and failure of planned elimination strategies is likely to discourage ongoing investment by funders. However, there has been very little modelling of malaria elimination and little direct involvement of policymakers in its development. There is thus an urgent need for user-friendly and accessible models purpose-designed in collaboration with policymakers to answer pertinent questions arising from the field.

RESULTS

An internet site is presented with a simple mathematical modelling platform for population level models of malaria elimination. It is freely accessible to all and designed to be flexible so both the platform and models can be developed through interaction with users. The site is an accessible introduction to modelling for a non-mathematical audience, and lessons learned from the project will help inform future development of mathematical models and improve communication of modelling results. Currently it hosts a simple model of strategies for malaria elimination and this will be developed, and more models added, over time. The iterative process of feedback and development will result in an educational and planning tool for non-modellers to assist with malaria elimination efforts worldwide.

CONCLUSIONS

By collaboration with end users, iterative development of mathematical models of malaria elimination through this internet platform will maximize its potential as an educational and public health policy planning tool. It will also assist with preliminary optimisation of local malaria elimination strategies before commitment of valuable resources.