Mathematical models of Plasmodium vivax transmission: A scoping review

Plasmodium vivax is one of the most geographically widespread malaria parasites in the world, primarily found across South-East Asia, Latin America, and parts of Africa. One of the significant characteristics of the P. vivax parasite is its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. Models that capture P. vivax dynamics differ from those that capture P. falciparum dynamics, as they must account for relapses caused by the activation of hypnozoites. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023. The primary objective of this work is to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. In doing so, we aim to assist researchers working on mathematical epidemiology, disease transmission, and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where further model development is required. We categorise P. vivax models according to whether a deterministic or agent-based approach was used. We provide an overview of the different strategies used to incorporate the parasite's biology, use of multiple scales (within-host and population-level), superinfection, immunity, and treatment interventions. In most of the published literature, the rationale for different modelling approaches was driven by the research question at hand. Some models focus on the parasites' complicated biology, while others incorporate simplified assumptions to avoid model complexity. Overall, the existing literature on mathematical models for P. vivax encompasses various aspects of the parasite's dynamics. We recommend that future research should focus on refining how key aspects of P. vivax dynamics are modelled, including spatial heterogeneity in exposure risk and heterogeneity in susceptibility to infection, the accumulation of hypnozoite variation, the interaction between P. falciparum and P. vivax, acquisition of immunity, and recovery under superinfection.

Quantifying the impact of interventions against Plasmodium vivax: A model for country-specific use

In order to evaluate the impact of various intervention strategies on Plasmodium vivax dynamics in low endemicity settings without significant seasonal pattern, we introduce a simple mathematical model that can be easily adapted to reported case numbers similar to that collected by surveillance systems in various countries. The model includes case management, vector control, mass drug administration and reactive case detection interventions and is implemented in both deterministic and stochastic frameworks. It is available as an R package to enable users to calibrate and simulate it with their own data. Although we only illustrate its use on fictitious data, by simulating and comparing the impact of various intervention combinations on malaria risk and burden, this model could be a useful tool for strategic planning, implementation and resource mobilization.

A model for malaria treatment evaluation in the presence of multiple species

Plasmodium falciparum and P. vivax are the two most common causes of malaria. While the majority of deaths and severe morbidity are due to P. falciparum, P. vivax poses a greater challenge to eliminating malaria outside of Africa due to its ability to form latent liver stage parasites (hypnozoites), which can cause relapsing episodes within an individual patient. In areas where P. falciparum and P. vivax are co-endemic, individuals can carry parasites of both species simultaneously. These mixed infections complicate dynamics in several ways: treatment of mixed infections will simultaneously affect both species, P. falciparum can mask the detection of P. vivax, and it has been hypothesised that clearing P. falciparum may trigger a relapse of dormant P. vivax. When mixed infections are treated for only blood-stage parasites, patients are at risk of relapse infections due to P. vivax hypnozoites. We present a stochastic mathematical model that captures interactions between P. falciparum and P. vivax, and incorporates both standard schizonticidal treatment (which targets blood-stage parasites) and radical cure treatment (which additionally targets liver-stage parasites). We apply this model via a hypothetical simulation study to assess the implications of different treatment coverages of radical cure for mixed and P. vivax infections and a "unified radical cure" treatment strategy where P. falciparum, P. vivax, and mixed infections all receive radical cure after screening glucose-6-phosphate dehydrogenase (G6PD) normal. In addition, we investigated the impact of mass drug administration (MDA) of blood-stage treatment. We find that a unified radical cure strategy leads to a substantially lower incidence of malaria cases and deaths overall. MDA with schizonticidal treatment was found to decrease P. falciparum with little effect on P. vivax. We perform a univariate sensitivity analysis to highlight important model parameters.

Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration

Plasmodium vivax is the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. One of the factors driving this widespread phenomenon is the ability of the parasites to remain dormant in the liver. Known as 'hypnozoites', they reside in the liver following an initial exposure, before activating later to cause further infections, referred to as 'relapses'. As around 79-96% of infections are attributed to relapses from activating hypnozoites, we expect it will be highly impactful to apply treatment to target the hypnozoite reservoir (i.e. the collection of dormant parasites) to eliminate P. vivax. Treatment with radical cure, for example tafenoquine or primaquine, to target the hypnozoite reservoir is a potential tool to control and/or eliminate P. vivax. We have developed a deterministic multiscale mathematical model as a system of integro-differential equations that captures the complex dynamics of P. vivax hypnozoites and the effect of hypnozoite relapse on disease transmission. Here, we use our multiscale model to study the anticipated effect of radical cure treatment administered via a mass drug administration (MDA) program. We implement multiple rounds of MDA with a fixed interval between rounds, starting from different steady-state disease prevalences. We then construct an optimisation model with three different objective functions motivated on a public health basis to obtain the optimal MDA interval. We also incorporate mosquito seasonality in our model to study its effect on the optimal treatment regime. We find that the effect of MDA interventions is temporary and depends on the pre-intervention disease prevalence (and choice of model parameters) as well as the number of MDA rounds under consideration. The optimal interval between MDA rounds also depends on the objective (combinations of expected intervention outcomes). We find radical cure alone may not be enough to lead to P. vivax elimination under our mathematical model (and choice of model parameters) since the prevalence of infection eventually returns to pre-MDA levels.

A Multiscale Mathematical Model of Plasmodium Vivax Transmission

Malaria is caused by Plasmodium parasites which are transmitted to humans by the bite of an infected Anopheles mosquito. Plasmodium vivax is distinct from other malaria species in its ability to remain dormant in the liver (as hypnozoites) and activate later to cause further infections (referred to as relapses). Mathematical models to describe the transmission dynamics of P. vivax have been developed, but most of them fail to capture realistic dynamics of hypnozoites. Models that do capture the complexity tend to involve many governing equations, making them difficult to extend to incorporate other important factors for P. vivax, such as treatment status, age and pregnancy. In this paper, we have developed a multiscale model (a system of integro-differential equations) that involves a minimal set of equations at the population scale, with an embedded within-host model that can capture the dynamics of the hypnozoite reservoir. In this way, we can gain key insights into dynamics of P. vivax transmission with a minimum number of equations at the population scale, making this framework readily scalable to incorporate more complexity. We performed a sensitivity analysis of our multiscale model over key parameters and found that prevalence of P. vivax blood-stage infection increases with both bite rate and number of mosquitoes but decreases with hypnozoite death rate. Since our mathematical model captures the complex dynamics of P. vivax and the hypnozoite reservoir, it has the potential to become a key tool to inform elimination strategies for P. vivax.

Investment case for malaria elimination in South Africa: a financing model for resource mobilization to accelerate regional malaria elimination

BACKGROUND

Malaria continues to be a public health problem in South Africa. While the disease is mainly confined to three of the nine provinces, most local transmissions occur because of importation of cases from neighbouring countries. The government of South Africa has reiterated its commitment to eliminate malaria within its borders. To support the achievement of this goal, this study presents a cost-benefit analysis of malaria elimination in South Africa through simulating different scenarios aimed at achieving malaria elimination within a 10-year period.

METHODS

A dynamic mathematical transmission model was developed to estimate the costs and benefits of malaria elimination in South Africa between 2018 and 2030. The model simulated a range of malaria interventions and estimated their impact on the transmission of Plasmodium falciparum malaria between 2018 and 2030 in the three endemic provinces of Limpopo, Mpumalanga and KwaZulu-Natal. Local financial, economic, and epidemiological data were used to calibrate the transmission model.

RESULTS

Based on the three primary simulated scenarios: Business as Usual, Accelerate and Source Reduction, the total economic burden was estimated as follows: for the Business as Usual scenario, the total economic burden of malaria in South Africa was R 3.69 billion (USD 223.3 million) over an 11-year period (2018-2029). The economic burden of malaria was estimated at R4.88 billion (USD 295.5 million) and R6.34 billion (~ USD 384 million) for the Accelerate and Source Reduction scenarios, respectively. Costs and benefits are presented in midyear 2020 values. Malaria elimination was predicted to occur in all three provinces if the Source Reduction strategy was adopted to help reduce malaria rates in southern Mozambique. This could be achieved by limiting annual local incidence in South Africa to less than 1 indigenous case with a prediction of this goal being achieved by the year 2026.

CONCLUSIONS

Malaria elimination in South Africa is feasible and economically worthwhile with a guaranteed positive return on investment (ROI). Findings of this study show that through securing funding for the proposed malaria interventions in the endemic areas of South Africa and neighbouring Mozambique, national elimination could be within reach in an 8-year period.

Operational research: A multidisciplinary approach for the management of infectious disease in a global context

Infectious diseases, both established and emerging, impose a significant burden globally. Successful management of infectious diseases requires considerable effort and a multidisciplinary approach to tackle the complex web of interconnected biological, public health and economic systems. Through a wide range of problem-solving techniques and computational methods, operational research can strengthen health systems and support decision-making at all levels of disease control. From improved understanding of disease biology, intervention planning and implementation, assessing economic feasibility of new strategies, identifying opportunities for cost reductions in routine processes, and informing health policy, this paper highlights areas of opportunity for operational research to contribute to effective and efficient infectious disease management and improved health outcomes.

Burden of communicable diseases and cost of illness: Asia pacific region

BACKGROUND

Communicable diseases such as AIDS/HIV, dengue fever, and malaria have a great burden and subsequent economic loss in the Asian region. The purpose of this article is to review the widespread burden of communicable diseases and related health-care burden for the patient in Asia and the Pacific.

AREAS COVERED

In Central Asia, the number of new AIDS cases increased by 29%. It is more endemic in the poor population with variations in the cost of illness. Dengue is prevalent in more than 100 countries, including the Asia-Pacific region. In Southeast Asia, the annual economic burden of dengue fever was between $ 610 and $ 1,384 million, with a per capita cost of $ 1.06 to $ 2.41. Globally, 2.9 billion people are at risk of developing malaria, 90% of whom are residents of the Asia and Pacific region. The annual per capita cost of malaria control ranged from $ 0.11 to $ 39.06 and for elimination from $ 0.18 to $ 27.

EXPERT OPINION

The cost of AIDS, dengue, and malaria varies from country to country due to different health-care systems. The literature review has shown that the cost of dengue disease and malaria is poorly documented.

Estimating the risk of declining funding for malaria in Ghana: the case for continued investment in the malaria response

BACKGROUND

Ghana has made impressive progress against malaria, decreasing mortality and morbidity by over 50% between 2005 and 2015. These gains have been facilitated in part, due to increased financial commitment from government and donors. Total resources for malaria increased from less than USD 25 million in 2006 to over USD 100 million in 2011. However, the country still faces a high burden of disease and is at risk of declining external financing due to its strong economic growth and the consequential donor requirements for increased government contributions. The resulting financial gap will need to be met domestically. The purpose of this study was to provide economic evidence of the potential risks of withdrawing financing to shape an advocacy strategy for resource mobilization.

METHODS

A compartmental transmission model was developed to estimate the impact of a range of malaria interventions on the transmission of Plasmodium falciparum malaria between 2018 and 2030. The model projected scenarios of common interventions that allowed the attainment of elimination and those that predicted transmission if interventions were withheld. The outputs of this model were used to generate costs and economic benefits of each option.

RESULTS

Elimination was predicted using the package of interventions outlined in the national strategy, particularly increased net usage and improved case management. Malaria elimination in Ghana is predicted to cost USD 961 million between 2020 and 2029. Compared to the baseline, elimination is estimated to prevent 85.5 million cases, save 4468 lives, and avert USD 2.2 billion in health system expenditures. The economic gain was estimated at USD 32 billion in reduced health system expenditure, increased household prosperity and productivity gains. Through malaria elimination, Ghana can expect to see a 32-fold return on their investment. Reducing interventions, predicted an additional 38.2 clinical cases, 2500 deaths and additional economic losses of USD 14.1 billion.

CONCLUSIONS

Malaria elimination provides robust epidemiological and economic benefits, however, sustained financing is need to accelerate the gains in Ghana. Although government financing has increased in the past decade, the amount is less than 25% of the total malaria financing. The evidence generated by this study can be used to develop a robust domestic strategy to overcome the financial barriers to achieving malaria elimination in Ghana.

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.

Simulating the council-specific impact of anti-malaria interventions: A tool to support malaria strategic planning in Tanzania

INTRODUCTION

The decision-making process for malaria control and elimination strategies has become more challenging. Interventions need to be targeted at council level to allow for changing malaria epidemiology and an increase in the number of possible interventions. Models of malaria dynamics can support this process by simulating potential impacts of multiple interventions in different settings and determining appropriate packages of interventions for meeting specific expected targets.

METHODS

The OpenMalaria model of malaria dynamics was calibrated for all 184 councils in mainland Tanzania using data from malaria indicator surveys, school parasitaemia surveys, entomological surveillance, and vector control deployment data. The simulations were run for different transmission intensities per region and five interventions, currently or potentially included in the National Malaria Strategic Plan, individually and in combination. The simulated prevalences were fitted to council specific prevalences derived from geostatistical models to obtain council specific predictions of the prevalence and number of cases between 2017 and 2020. The predictions were used to evaluate in silico the feasibility of the national target of reaching a prevalence of below 1% by 2020, and to suggest alternative intervention stratifications for the country.

RESULTS

The historical prevalence trend was fitted for each council with an agreement of 87% in 2016 (95%CI: 0.84-0.90) and an agreement of 90% for the historical trend (2003-2016) (95%CI: 0.87-0.93) The current national malaria strategy was expected to reduce the malaria prevalence between 2016 and 2020 on average by 23.8% (95% CI: 19.7%-27.9%) if current case management levels were maintained, and by 52.1% (95% CI: 48.8%-55.3%) if the case management were improved. Insecticide treated nets and case management were the most cost-effective interventions, expected to reduce the prevalence by 25.0% (95% CI: 19.7%-30.2) and to avert 37 million cases between 2017 and 2020. Mass drug administration was included in most councils in the stratification selected for meeting the national target at minimal costs, expected to reduce the prevalence by 77.5% (95%CI: 70.5%-84.5%) and to avert 102 million cases, with almost twice higher costs than those of the current national strategy. In summary, the model suggested that current interventions are not sufficient to reach the national aim of a prevalence of less than 1% by 2020 and a revised strategic plan needs to consider additional, more effective interventions, especially in high transmission areas and that the targets need to be revisited.

CONCLUSION

The methodology reported here is based on intensive interactions with the NMCP and provides a helpful tool for assessing the feasibility of country specific targets and for determining which intervention stratifications at sub-national level will have most impact. This country-led application could support strategic planning of malaria control in many other malaria endemic countries.