Within-host modeling of blood-stage malaria

Red blood cell dynamics during malaria infection violate the assumptions of mathematical models of infection dynamics

For decades, mathematical models have been used to understand the course and outcome of malaria infections (i.e., infection dynamics) and the evolutionary dynamics of the parasites that cause them. A key conclusion of these models is that red blood cell (RBC) availability is a fundamental driver of infection dynamics and parasite trait evolution. The extent to which this conclusion holds will in part depend on model assumptions about the host-mediated processes that regulate RBC availability i.e., removal of uninfected RBCs and supply of RBCs. Diverse mathematical functions have been used to describe host-mediated RBC supply and clearance, but it remains unclear whether they adequately capture the dynamics of RBC supply and clearance during infection. Here, we use a unique dataset, comprising time-series measurements of erythrocyte (i.e., mature RBC) and reticulocyte (i.e., newly supplied RBC) densities during Plasmodium chabaudi malaria infection, and a quantitative data-transformation scheme to elucidate whether RBC dynamics conform to common model assumptions. We found that RBC clearance and supply are not well described by mathematical functions commonly used to model these processes. Furthermore, the temporal dynamics of both processes vary with parasite growth rate in a manner again not captured by existing models. Together, these finding suggest that new model formulations are required if we are to explain and ultimately predict the within-host population dynamics and evolution of malaria parasites.

Multi-omics dissection of stage-specific artemisinin tolerance mechanisms in Kelch13-mutant Plasmodium falciparum

AIMS

We investigated the stage-specific mechanisms of partial resistance to artemisinin (ART, an antimalarial drug) in Plasmodium falciparum (P. falciparum) carrying the Kelch13 C580Y mutation.

METHODS

Using fluorescence labeling and activity-based protein profiling, we systematically profile the ART activation levels in P. falciparum during the entire intra-erythrocytic developmental cycle (IDC), and determined the ART-targets profile of the ART-sensitive and -resistant strains at different stages. We retrieved and integrated datasets of single-cell transcriptomics and label-free proteomics across three IDC stages of wild-type P. falciparum. We also employed lipidomics to validate lipid metabolic reprogramming in the resistant strain.

RESULTS

The activation and expression patterns of genes and proteins of ART-targets in both ART-sensitive and resistant strains varied at different stages and periods of P. falciparum development, with the late trophozoite stage harboring the largest number of ART targets. We identified and validated 36 overlapping targets, such as GAPDH, EGF-1a, and SpdSyn, during the IDC stages in both strains. We revealed the ART-insensitivity of fatty acid-associated activities in the partially resistant strain at both the early ring and early trophozoite stages.

CONCLUSIONS

Our multi-omics strategies provide novel insights into the mechanisms of ART partial resistance in Kelch13 mutant P. falciparum, demonstrating the stage-specific interaction between ART and malaria parasites.

Modeling the contribution of antibody attack rates to single and dual helminth infections in a natural system

Within-host models of infection can provide important insights into the processes that affect parasite spread and persistence in host populations. However, modeling can be limited by the availability of empirical data, a problem commonly encountered in natural systems. Here, we used six years of immune-infection observations of two gastrointestinal helminths (Trichostrongylus retortaeformis and Graphidium strigosum) from a population of European rabbits (Oryctolagus cuniculus) to develop an age-dependent, mathematical model that explicitly included species-specific and cross-reacting antibody (IgA and IgG) responses to each helminth in hosts with single or dual infections. Different models of single infection were formally compared to test alternative mechanisms of parasite regulation. The two models that best described single infections of each helminth species were then coupled through antibody cross-immunity to examine how the presence of one species could alter the host immune response to, and the within-host dynamics of, the other species. For both single infections, model selection suggested that either IgA or IgG responses could equally explain the observed parasite intensities by host age. However, the antibody attack rate and affinity level changed between the two helminths, it was stronger against T. retortaeformis than against G. strigosum and caused contrasting age-intensity profiles. When the two helminths coinfect the same host, we found variation of the species-specific antibody response to both species together with an asymmetric cross-immune response driven by IgG. Lower attack rate and affinity of antibodies in dual than single infections contributed to the significant increase of both helminth intensities. By combining mathematical modeling with immuno-infection data, our work provides a tractable model framework for disentangling some of the complexities generated by host-parasite and parasite-parasite interactions in natural systems.

Global dynamics of SARS-CoV-2/malaria model with antibody immune response

Coronavirus disease 2019 (COVID-19) is a new viral disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Malaria is a parasitic disease caused by Plasmodium parasites. In this paper, we explore a within-host model of SARS-CoV-2/malaria coinfection. This model consists of seven ordinary differential equations that study the interactions between uninfected red blood cells, infected red blood cells, free merozoites, uninfected epithelial cells, infected epithelial cells, free SARS-CoV-2 particles, and antibodies. We show that the model has bounded and nonnegative solutions. We compute all steady state points and derive their existence conditions. We use appropriate Lyapunov functions to confirm the global stability of all steady states. We enhance the reliability of the theoretical results by performing numerical simulations. The steady states reflect the monoinfection and coinfection with malaria and SARS-CoV-2. The shared immune response reduces the concentrations of malaria merozoites and SARS-CoV-2 particles in coinfected patients. This response reduces the severity of SARS-CoV-2 infection in this group of patients.

Motivation to test, treat, and report malaria cases: a quantitative assessment among private sector providers in the Greater Mekong Subregion

Background

Accurately testing, treating, and tracking all malaria cases is critical to achieving elimination. Ensuring health providers are able and motivated to test, treat, and report cases is a necessary component of elimination programmes, and particularly challenging in low endemic settings where providers may not encounter a large volume of cases. This study aimed to understand provider motivations to test, treat, and report malaria cases to better optimize programme design, adjust incentive schemes, and ultimately improve reporting rates while growing the evidence base around private providers in the Greater Mekong Subregion (GMS).

Methods

With funding from the Bill & Melinda Gates Foundation, this study aimed to identify and validate distinctive subtypes of motivation among private sector providers enrolled in the Greater Mekong Subregion Elimination of Malaria through Surveillance (GEMS) programme, implemented by Population Services International. Quantitative questionnaires were administered electronically in person by trained enumerators to various provider groups in Myanmar, Lao PDR, and Vietnam. A three-stage confirmatory factor analysis was then conducted in STATA.

Results

Following this analysis, a two-factor solution that describes motivation in this population of providers was identified, and providers were scored on the two dimensions of motivation. The correlation between the two rotated factors was 0.3889, and the Kaiser–Meyer–Olkin (KMO) measure of sampling adequacy was 0.93, indicating an excellent level of suitability. These providers, who are often assumed to only be financially motivated, engaged in malaria elimination activities because of both internal and external motivational factors that are independent of remuneration or financial gain. For all three countries’ data, significant covariances between the two latent variables for internal and external motivation were found. The models were found to be of adequate to good fit for the data across all three countries. It was determined that private sector providers, who were previously believed to be primarily financially motivated, were also motivated by personal factors. Motivation was also associated with key outcomes of importance to malaria elimination, such as reporting and stocking of tests and treatments.

Conclusion

Maintaining or increasing provider motivation to test and treat is essential in the fight to eliminate malaria from the GMS, as it helps to ensure that providers continue to pursue this goal, even in a low incidence environment where cases may be rare and in which providers face financial pressure to focus on areas of health service provision. Establishing mechanisms to better motivate providers through intrinsic factors is likely to have a substantive impact on the sustainability of malaria case management activities.

Understanding dynamics of Plasmodium falciparum gametocytes production: Insights from an age-structured model

Many models of within-host malaria infection dynamics have been formulated since the pioneering work of Anderson et al. in 1989. Biologically, the goal of these models is to understand what governs the severity of infections, the patterns of infectiousness, and the variation thereof across individual hosts. Mathematically, these models are based on dynamical systems, with standard approaches ranging from K-compartments ordinary differential equations (ODEs) to delay differential equations (DDEs), to capture the relatively constant duration of replication and bursting once a parasite infects a host red blood cell. Using malariatherapy data, which offers fine-scale resolution on the dynamics of infection across a number of individual hosts, we compare the fit and robustness of one of these standard approaches (K-compartments ODE) with a partial differential equations (PDEs) model, which explicitly tracks the "age" of an infected cell. While both models perform quite similarly in terms of goodness-of-fit for suitably chosen K, the K-compartments ODE model particularly overestimates parasite densities early on in infections when the number of repeated compartments is not large enough. Finally, the K-compartments ODE model (for suitably chosen K) and the PDE model highlight a strong qualitative connection between the density of transmissible parasite stages (i.e., gametocytes) and the density of host-damaging (and asexually-replicating) parasite stages. This finding provides a simple tool for predicting which hosts are most infectious to mosquitoes -vectors of Plasmodium parasites- which is a crucial component of global efforts to control and eliminate malaria.

MULTIPLE PERIODIC SOLUTIONS OF A WITHIN-HOST MALARIA INFECTION MODEL WITH TIME DELAY

In this paper, we study a within-host malaria infection model recently proposed by Schneider et al. in 2018. The stability and Hopf bifurcation analysis at the interior equilibrium are carried out, finding that the basic reproduction number plays a key role in the dynamics of the model, and incrementing the time delay will induce Hopf bifurcation at this equilibrium. The global extension of the local Hopf branch is further tracked numerically by the MatLab package DDE-BIFTOOL. Neimark-Sacker bifurcation of Poincaré map and period-doubling bifurcation of the bifurcated periodic solution are also detected, resulting in the existence of quasi-periodic and multiple periodic solutions, respectively. These results reveal that Hopf bifurcation will indeed bring about the rich dynamics of the model.

Deconstructing the parasite multiplication rate of Plasmodium falciparum

Epidemiological indicators describing population-level malaria transmission dynamics are widely used to guide policy recommendations. However, the determinants of malaria outcomes within individuals are still poorly understood. This conceptual gap partly reflects the fact that there are few indicators that robustly predict the trajectory of individual infections or clinical outcomes. The parasite multiplication rate (PMR) is a widely used indicator for the Plasmodium intraerythrocytic development cycle (IDC), for example, but its relationship to clinical outcomes is complex. Here, we review its calculation and use in P. falciparum malaria research, as well as the parasite and host factors that impact it. We also provide examples of metrics that can help to link within-host dynamics to malaria clinical outcomes when used alongside the PMR.

Physiological and Pathological Inflammation Induced by Antibodies and Pentraxins

Macrophages play a key role in induction of inflammatory responses. These inflammatory responses are mostly considered to be instigated by activation of pattern recognition receptors (PRRs) or cytokine receptors. However, recently it has become clear that also antibodies and pentraxins, which can both activate Fc receptors (FcRs), induce very powerful inflammatory responses by macrophages that can even be an order of magnitude greater than PRRs. While the physiological function of this antibody-dependent inflammation (ADI) is to counteract infections, undesired activation or over-activation of this mechanism will lead to pathology, as observed in a variety of disorders, including viral infections such as COVID-19, chronic inflammatory disorders such as Crohn's disease, and autoimmune diseases such as rheumatoid arthritis. In this review we discuss how physiological ADI provides host defense by inducing pathogen-specific immunity, and how erroneous activation of this mechanism leads to pathology. Moreover, we will provide an overview of the currently known signaling and metabolic pathways that underlie ADI, and how these can be targeted to counteract pathological inflammation.

Parasite-Host Dynamics throughout Antimalarial Drug Development Stages Complicate the Translation of Parasite Clearance

Ensuring continued success against malaria depends on a pipeline of new antimalarials. Antimalarial drug development utilizes preclinical murine and experimental human malaria infection studies to evaluate drug efficacy.

Ensuring continued success against malaria depends on a pipeline of new antimalarials. Antimalarial drug development utilizes preclinical murine and experimental human malaria infection studies to evaluate drug efficacy. A sequential approach is typically adapted, with results from each stage informing the design of the next stage of development. The validity of this approach depends on confidence that results from murine malarial studies predict the outcome of clinical trials in humans. Parasite clearance rates following treatment are key parameters of drug efficacy. To investigate the validity of forward predictions, we developed a suite of mathematical models to capture parasite growth and drug clearance along the drug development pathway and estimated parasite clearance rates. When comparing the three infection experiments, we identified different relationships of parasite clearance with dose and different maximum parasite clearance rates. In Plasmodium berghei-NMRI mouse infections, we estimated a maximum parasite clearance rate of 0.2 (1/h); in Plasmodium falciparum-SCID mouse infections, 0.05 (1/h); and in human volunteer infection studies with P. falciparum, we found a maximum parasite clearance rate of 0.12 (1/h) and 0.18 (1/h) after treatment with OZ439 and MMV048, respectively. Sensitivity analysis revealed that host-parasite driven processes account for up to 25% of variance in parasite clearance for medium-high doses of antimalarials. Although there are limitations in translating parasite clearance rates across these experiments, they provide insight into characterizing key parameters of drug action and dose response and assist in decision-making regarding dosage for further drug development.

Therapeutic Efficacy of Artemether-Lumefantrine for Uncomplicated Falciparum Malaria in Northern Zambia

Artemether-lumefantrine (AL) is a first-line agent for uncomplicated malaria caused by Plasmodium falciparum. The WHO recommends periodic therapeutic efficacy studies of antimalarial drugs for the detection of malaria parasite drug resistance and to inform national malaria treatment policies. We conducted a therapeutic efficacy study of AL in a high malaria transmission region of northern Zambia from December 2014 to July 2015. One hundred children of ages 6 to 59 months presenting to a rural health clinic with uncomplicated falciparum malaria were admitted for treatment with AL (standard 6-dose regimen) and followed weekly for 5 weeks. Parasite counts were taken every 6 hours during treatment to assess parasite clearance. Recurrent episodes during follow-up (n = 14) were genotyped to distinguish recrudescence from reinfection and to identify drug resistance single nucleotide polymorphisms (SNPs) and multidrug resistance protein 1 (mdr1) copy number variation. Day 7 lumefantrine concentrations were measured for correspondence with posttreatment reinfection. All children who completed the parasite clearance portion of the study (n = 94) were microscopy-negative by 72 hours. The median parasite elimination half-life was 2.7 hours (interquartile range: 2.1-3.3). Genotype-corrected therapeutic efficacy was 98.8% (95% CI: 97.6-100). Purported artemisinin and lumefantrine drug resistance SNPs in atp6, 3D7_1451200, and mdr1 were detected but did not correlate with parasite recurrence, nor did day 7 lumefantrine concentrations. In summary, AL was highly effective for the treatment of uncomplicated falciparum malaria in northern Zambia during the study period. The high incidence of recurrent parasitemia was consistent with reinfection due to high, perennial malaria transmission.

Leveraging Computational Modeling to Understand Infectious Diseases

Purpose of Review

Computational and mathematical modeling have become a critical part of understanding in-host infectious disease dynamics and predicting effective treatments. In this review, we discuss recent findings pertaining to the biological mechanisms underlying infectious diseases, including etiology, pathogenesis, and the cellular interactions with infectious agents. We present advances in modeling techniques that have led to fundamental disease discoveries and impacted clinical translation.

Recent Findings

Combining mechanistic models and machine learning algorithms has led to improvements in the treatment of Shigella and tuberculosis through the development of novel compounds. Modeling of the epidemic dynamics of malaria at the within-host and between-host level has afforded the development of more effective vaccination and antimalarial therapies. Similarly, in-host and host-host models have supported the development of new HIV treatment modalities and an improved understanding of the immune involvement in influenza. In addition, large-scale transmission models of SARS-CoV-2 have furthered the understanding of coronavirus disease and allowed for rapid policy implementations on travel restrictions and contract tracing apps.

Summary

Computational modeling is now more than ever at the forefront of infectious disease research due to the COVID-19 pandemic. This review highlights how infectious diseases can be better understood by connecting scientists from medicine and molecular biology with those in computer science and applied mathematics.

Global analysis of a reaction–diffusion blood-stage malaria model with immune response

Malaria is one of the most dangerous diseases that threatens people’s lives around the world. In this paper, we study a reaction-diffusion model for the within-host dynamics of malaria infection with an antibody immune response. The model is given by a system of partial differential equations (PDEs) to describe the blood-stage of malaria life cycle. It addresses the interactions between uninfected red blood cells, antibodies, and three types of infected red blood cells, namely ring-infected red blood cells, trophozoite-infected red blood cells and schizont-infected red blood cells. Moreover, the model contains a parameter to measure the efficacy of isoleucine starvation and its effect on the growth of malaria parasites. We show the basic properties of the model. We compute all equilibria and derive the thresholds from the conditions of existence of malaria equilibrium points. We prove the global stability of all equilibrium points based on choosing suitable Lyapunov functionals. We use the characteristic equations to verify the local instability of equilibrium points. We finally execute numerical simulations to validate the theoretical results and highlight some important observations. The results indicate that isoleucine starvation can have a critical impact on the stability of equilibrium points. When the efficacy of isoleucine starvation is high, it switches the system from the infection state to the malaria-free state. The presence of an antibody immune response does not lead to the elimination of malaria infection, but it suppresses the growth of malaria parasites and increases the amount of healthy red blood cells.

Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response

Malaria is one of the most dangerous global diseases. This paper studies a reaction-diffusion model for the within-host dynamics of malaria infection with both antibody and cell-mediated immune responses. The model explores the interactions between uninfected red blood cells (erythrocytes), three types of infected red blood cells, free merozoites, CTLs and antibodies. It contains some parameters to measure the effect of antimalarial drugs and isoleucine starvation on the blood cycle of malaria infection. The basic properties of the model are discussed. All possible equilibrium points and the threshold conditions required for their existence are addressed. The global stability of all equilibria are proved by selecting suitable Lyapunov functionals and using LaSalle’s invariance principle. The characteristic equations are used to study the local instability conditions of the equilibria. Some numerical simulations are conducted to support the theoretical results. The results indicate that antimalarial drugs with high efficacy can clear the infection and take the system towards the disease-free state. Increasing the efficacy of isoleucine starvation has a similar effect as antimalarial drugs and can eliminate the disease. The presence of immune responses with low efficacy of treatments does not provide a complete protection against the disease. However, the immune responses reduce the concentrations of all types of infected cells and limit the production of malaria parasites.

Role of a Concentration Gradient in Malaria Drug Resistance Evolution: A Combined within- and between-Hosts Modelling Approach

Resistance to antimalarial drugs is currently a growing public health problem, resulting in more cases with treatment failure. Although previous studies suggested that a concentration gradient facilitates the antibiotic resistance evolution in bacteria, no attempt has been made to investigate the roles of a concentration gradient in malaria drug resistance. Unlike the person-to-person mode of transmission of bacteria, the malaria parasites need to switch back and forth between the human and mosquito hosts to complete the life cycle and to spread the resistant alleles. Here we developed a stochastic combined within- and between-hosts evolutionary dynamics model specific to malaria parasites in order to investigate the influence of an antimalarial concentration gradient on the evolutionary dynamics of malaria drug resistance. Every stage of malaria development in both human and mosquito hosts are individually modelled using the tau-leaping algorithm. We found that the concentration gradient can accelerate antimalarial resistance evolution. The gain in resistance evolution was improved by the increase in the parasite mutation rate and the mosquito biting rate. In addition, even though the rate of resistance evolution is not sensitive to the changes in parasite reduction ratios (PRRs) of antimalarial drugs, the probability of finding the antimalarial drug resistant parasites decreases when the PRR increases.

Malaria Parasite Clearance: What Are We Really Measuring?

Antimalarial drugs are vital for treating malaria and controlling transmission. Measuring drug efficacy in the field requires large clinical trials and thus we have identified proxy measures of drug efficacy such as the parasite clearance curve. This is often assumed to measure the rate of drug activity against parasites and is used to predict optimal treatment regimens required to completely clear a blood-stage infection. We discuss evidence that the clearance curve is not measuring the rate of drug killing. This has major implications for how we assess optimal treatment regimens, as well as how we prioritise new drugs in the drug development pipeline.

Ensemble modeling highlights importance of understanding parasite-host behavior in preclinical antimalarial drug development

Emerging drug resistance and high-attrition rates in early and late stage drug development necessitate accelerated development of antimalarial compounds. However, systematic and meaningful translation of drug efficacy and host-parasite dynamics between preclinical testing stages is missing. We developed an ensemble of mathematical within-host parasite growth and antimalarial action models, fitted to extensive data from four antimalarials with different modes of action, to assess host-parasite interactions in two preclinical drug testing systems of murine parasite P. berghei in mice, and human parasite P. falciparum in immune-deficient mice. We find properties of the host-parasite system, namely resource availability, parasite maturation and virulence, drive P. berghei dynamics and drug efficacy, whereas experimental constraints primarily influence P. falciparum infection and drug efficacy. Furthermore, uninvestigated parasite behavior such as dormancy influences parasite recrudescence following non-curative treatment and requires further investigation. Taken together, host-parasite interactions should be considered for meaningful translation of pharmacodynamic properties between murine systems and for predicting human efficacious treatment.

Modeling the dynamics of Plasmodium falciparum gametocytes in humans during malaria infection

Renewed efforts to eliminate malaria have highlighted the potential to interrupt human-to-mosquito transmission — a process mediated by gametocyte kinetics in human hosts. Here we study the in vivo dynamics of Plasmodium falciparum gametocytes by establishing a framework which incorporates improved measurements of parasitemia, a novel gametocyte dynamics model and model fitting using Bayesian hierarchical inference. We found that the model provides an excellent fit to the clinical data from 17 volunteers infected with P. falciparum (3D7 strain) and reliably predicts observed gametocytemia. We estimated the sexual commitment rate and gametocyte sequestration time to be 0.54% (95% credible interval: 0.30–1.00%) per asexual replication cycle and 8.39 (6.54–10.59) days respectively. We used the data-calibrated model to investigate human-to-mosquito transmissibility, providing a method to link within-human host infection kinetics to epidemiological-scale infection and transmission patterns.

Analysis of erythrocyte dynamics in Rhesus macaque monkeys during infection with Plasmodium cynomolgi

BACKGROUND

Malaria is a major mosquito transmitted, blood-borne parasitic disease that afflicts humans. The disease causes anaemia and other clinical complications, which can lead to death. Plasmodium vivax is known for its reticulocyte host cell specificity, but many gaps in disease details remain. Much less is known about the closely related species, Plasmodium cynomolgi, although it is naturally acquired and causes zoonotic malaria. Here, a computational model is developed based on longitudinal analyses of P. cynomolgi infections in nonhuman primates to investigate the erythrocyte dynamics that is pertinent to understanding both P. cynomolgi and P. vivax malaria in humans.

METHODS

A cohort of five P. cynomolgi infected Rhesus macaques (Macaca mulatta) is studied, with individuals exhibiting a plethora of clinical outcomes, including varying levels of anaemia. A discrete recursive model with age structure is developed to replicate the dynamics of P. cynomolgi blood-stage infections. The model allows for parasitic reticulocyte preference and assumes an age preference among the mature RBCs. RBC senescence is modelled using a hazard function, according to which RBCs have a mean lifespan of 98 ± 21 days.

RESULTS

Based on in vivo data from three cohorts of macaques, the computational model is used to characterize the reticulocyte lifespan in circulation as 24 ± 5 h (n = 15) and the rate of RBC production as 2727 ± 209 cells/h/µL (n = 15). Analysis of the host responses reveals a pre-patency increase in the number of reticulocytes. It also allows the quantification of RBC removal through the bystander effect.

CONCLUSIONS

The evident pre-patency increase in reticulocytes is due to a shift towards the release of younger reticulocytes, which could result from a parasite-induced factor meant to increase reticulocyte availability and satisfy the parasite's tropism, which has an average value of 32:1 in this cohort. The number of RBCs lost due to the bystander effect relative to infection-induced RBC losses is 62% for P. cynomolgi infections, which is substantially lower than the value of 95% previously determined for another simian species, Plasmodium coatneyi.