From within host dynamics to the epidemiology of infectious disease: Scientific overview and challenges

The role of natural recovery category in malaria dynamics under saturated treatment

In the process of malaria transmission, natural recovery individuals are slightly infectious compared with infected individuals. Our concern is whether the infectivity of natural recovery category can be ignored in areas with limited medical resources, so as to reveal the epidemic pattern of malaria with simpler analysis. To achieve this, we incorporate saturated treatment into two-compartment and three-compartment models, and the infectivity of natural recovery category is only reflected in the latter. The non-spatial two-compartment model can admit backward bifurcation. Its spatial version does not possess rich dynamics. Besides, the non-spatial three-compartment model can undergo backward bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. For spatial three-compartment model, due to the complexity of characteristic equation, we apply Shengjin's Distinguishing Means to realize stability analysis. Further, the model exhibits Turing instability, Hopf bifurcation and Turing-Hopf bifurcation. This makes the model may admit bistability or even tristability when its basic reproduction number less than one. Biologically, malaria may present a variety of epidemic trends, such as elimination or inhomogeneous distribution in space and periodic fluctuation in time of infectious populations. Notably, parameter regions are given to illustrate substitution effect of two-compartment model for three-compartment model in both scenarios without or with spatial movement. Finally, spatial three-compartment model is used to present malaria transmission in Burundi. The application of efficiency index enables us to determine the most effective method to control the number of cases in different scenarios.

Development and Analysis of Multiscale Models for Tuberculosis: From Molecules to Populations

Although infectious disease dynamics are often analyzed at the macro-scale, increasing numbers of drug-resistant infections highlight the importance of within-host modeling that simultaneously solves across multiple scales to effectively respond to epidemics. We review multiscale modeling approaches for complex, interconnected biological systems and discuss critical steps involved in building, analyzing, and applying such models within the discipline of model credibility. We also present our two tools: CaliPro, for calibrating multiscale models (MSMs) to datasets, and tunable resolution, for fine- and coarse-graining sub-models while retaining insights. We include as an example our work simulating infection with Mycobacterium tuberculosis to demonstrate modeling choices and how predictions are made to generate new insights and test interventions. We discuss some of the current challenges of incorporating novel datasets, rigorously training computational biologists, and increasing the reach of MSMs. We also offer several promising future research directions of incorporating within-host dynamics into applications ranging from combinatorial treatment to epidemic response.

Mathematical models of cystic fibrosis as a systemic disease

Cystic fibrosis (CF) is widely known as a disease of the lung, even though it is in truth a systemic disease, whose symptoms typically manifest in gastrointestinal dysfunction first. CF ultimately impairs not only the pancreas and intestine but also the lungs, gonads, liver, kidneys, bones, and the cardiovascular system. It is caused by one of several mutations in the gene of the epithelial ion channel protein CFTR. Intense research and improved antimicrobial treatments during the past eight decades have steadily increased the predicted life expectancy of a person with CF (pwCF) from a few weeks to over 50 years. Moreover, several drugs ameliorating the sequelae of the disease have become available in recent years, and notable treatments of the root cause of the disease have recently generated substantial improvements in health for some but not all pwCF. Yet, numerous fundamental questions remain unanswered. Complicating CF, for instance in the lung, is the fact that the associated insufficient chloride secretion typically perturbs the electrochemical balance across epithelia and, in the airways, leads to the accumulation of thick, viscous mucus and mucus plaques that cannot be cleared effectively and provide a rich breeding ground for a spectrum of bacterial and fungal communities. The subsequent infections often become chronic and respond poorly to antibiotic treatments, with outcomes sometimes only weakly correlated with the drug susceptibility of the target pathogen. Furthermore, in contrast to rapidly resolved acute infections with a single target pathogen, chronic infections commonly involve multi-species bacterial communities, called "infection microbiomes," that develop their own ecological and evolutionary dynamics. It is presently impossible to devise mathematical models of CF in its entirety, but it is feasible to design models for many of the distinct drivers of the disease. Building upon these growing yet isolated modeling efforts, we discuss in the following the feasibility of a multi-scale modeling framework, known as template-and-anchor modeling, that allows the gradual integration of refined sub-models with different granularity. The article first reviews the most important biomedical aspects of CF and subsequently describes mathematical modeling approaches that already exist or have the potential to deepen our understanding of the multitude aspects of the disease and their interrelationships. The conceptual ideas behind the approaches proposed here do not only pertain to CF but are translatable to other systemic diseases. This article is categorized under: Congenital Diseases > Computational Models.

Systems biology of malaria explored with nonhuman primates

"The Primate Malarias" book has been a uniquely important resource for multiple generations of scientists, since its debut in 1971, and remains pertinent to the present day. Indeed, nonhuman primates (NHPs) have been instrumental for major breakthroughs in basic and pre-clinical research on malaria for over 50 years. Research involving NHPs have provided critical insights and data that have been essential for malaria research on many parasite species, drugs, vaccines, pathogenesis, and transmission, leading to improved clinical care and advancing research goals for malaria control, elimination, and eradication. Whilst most malaria scientists over the decades have been studying Plasmodium falciparum, with NHP infections, in clinical studies with humans, or using in vitro culture or rodent model systems, others have been dedicated to advancing research on Plasmodium vivax, as well as on phylogenetically related simian species, including Plasmodium cynomolgi, Plasmodium coatneyi, and Plasmodium knowlesi. In-depth study of these four phylogenetically related species over the years has spawned the design of NHP longitudinal infection strategies for gathering information about ongoing infections, which can be related to human infections. These Plasmodium-NHP infection model systems are reviewed here, with emphasis on modern systems biological approaches to studying longitudinal infections, pathogenesis, immunity, and vaccines. Recent discoveries capitalizing on NHP longitudinal infections include an advanced understanding of chronic infections, relapses, anaemia, and immune memory. With quickly emerging new technological advances, more in-depth research and mechanistic discoveries can be anticipated on these and additional critical topics, including hypnozoite biology, antigenic variation, gametocyte transmission, bone marrow dysfunction, and loss of uninfected RBCs. New strategies and insights published by the Malaria Host-Pathogen Interaction Center (MaHPIC) are recapped here along with a vision that stresses the importance of educating future experts well trained in utilizing NHP infection model systems for the pursuit of innovative, effective interventions against malaria.

The role of a programmatic immune response on the evolution of pathogen traits

In modelling pathogen evolution during epidemics, it is important to understand the interactions between within-host infection dynamics and between-host pathogen transmission. Multiscale models often assume an immune response that is highly responsive to pathogen dynamics. Empirical evidence, however, suggests that the immune response in acute infections is triggered and programmatic. This leads to somewhat more predictable infection trajectories where transition times and, consequently, the infectious window are non-exponentially distributed. Here, we develop a within-host model where the immune response is triggered by pathogen growth but otherwise develops independently, and use this to obtain analytic expressions for the infectious period and peak pathogen load. This allows us to model the basic reproductive number in terms of explicit functional relationships among within-host traits including the growth rate of the pathogen. We find that the dependence of pathogen load and the infectious window on within-host parameters constrains the evolution of the pathogen growth rate. At low growth rate, selection favours a higher pathogen load and therefore increasing pathogen growth rate. At high growth rates, selection for a longer infectious window trades off against selection against the effects of virulence. At intermediate growth rates the basic reproductive number is relatively insensitive to changes in the growth rate. The resulting "flat" region of the pathogen fitness landscape is due to the stability of the programmatic immune response in clearing the infection.

Multi-omics approaches to improve malaria therapy

Malaria contributes to the most widespread infectious diseases worldwide. Even though current drugs are commercially available, the ever-increasing drug resistance problem by malaria parasites poses new challenges in malaria therapy. Hence, searching for efficient therapeutic strategies is of high priority in malaria control. In recent years, multi-omics technologies have been extensively applied to provide a more holistic view of functional principles and dynamics of biological mechanisms. We briefly review multi-omics technologies and focus on recent malaria progress conducted with the help of various omics methods. Then, we present up-to-date advances for multi-omics approaches in malaria. Next, we describe resistance phenomena to established antimalarial drugs and underlying mechanisms. Finally, we provide insight into novel multi-omics approaches, new drugs and vaccine developments and analyze current gaps in multi-omics research. Although multi-omics approaches have been successfully used in malaria studies, they are still limited. Many gaps need to be filled to bridge the gap between basic research and treatment of malaria patients. Multi-omics approaches will foster a better understanding of the molecular mechanisms of Plasmodium that are essential for the development of novel drugs and vaccines to fight this disastrous disease.

Modeling and analysis of different scenarios for the spread of COVID-19 by using the modified multi-agent systems - Evidence from the selected countries

Currently, there is a global pandemic of COVID-19. To assess its prevalence, it is necessary to have adequate models that allow real-time modeling of the impact of various quarantine measures by the state. The SIR model, which is implemented using a multi-agent system based on mobile cellular automata, was improved. The paper suggests ways to improve the rules of the interaction and behavior of agents. Methods of comparing the parameters of the SIR model with real geographical, social and medical indicators have been developed. That allows the modeling of the spatial distribution of COVID-19 as a single location and as the whole country consisting of individual regions that interact with each other by transport, taking into account factors such as public transport, supermarkets, schools, universities, gyms, churches, parks. The developed model also allows us to assess the impact of quarantine, restrictions on transport connections between regions, to take into account such factors as the incubation period, the mask regime, maintaining a safe distance between people, and so on. A number of experiments were conducted in the work, which made it possible to assess both the impact of individual measures to stop the pandemic and their comprehensive application. A method of comparing computer-time and dynamic parameters of the model with real data is proposed, which allowed assessing the effectiveness of the government in stopping the pandemic in the Chernivtsi region, Ukraine. A simulation of the pandemic spread in countries such as Slovakia, Turkey and Serbia was also conducted. The calculations showed the high-accuracy matching of the forecast model with real data.

A hybrid multi-scale model of COVID-19 transmission dynamics to assess the potential of non-pharmaceutical interventions

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel coronavirus that emerged in Wuhan, China in December 2019. It has caused a global outbreak which represents a major threat to global health. Public health resorted to non-pharmaceutical interventions such as social distancing and lockdown to slow down the spread of the pandemic. However, the effect of each of these measures remains hard to quantify. We design a multi-scale model that simulates the transmission dynamics of COVID-19. We describe the motion of individual agents using a social force model. Each agent can be either susceptible, infected, quarantined, immunized or deceased. The model considers both mechanisms of direct and indirect transmission. We parameterize the model to reproduce the early dynamics of disease spread in Italy. We show that panic situations increase the risk of infection transmission in crowds despite social distancing measures. Next, we reveal that pre-symptomatic transmission accelerates the onset of the exponential growth of cases. After that, we demonstrate that the persistence of SARS-CoV-2 on hard surfaces determines the number of cases reached during the peak of the epidemic. Then, we show that the restricted movement of the individuals flattens the epidemic curve. Finally, model predictions suggest that measures stricter than social distancing and lockdown were used to control the epidemic in Wuhan, China.

Functional genomics of simian malaria parasites and host-parasite interactions

Two simian malaria parasite species, Plasmodium knowlesi and Plasmodium cynomolgi, cause zoonotic infections in Southeast Asia, and they have therefore gained recognition among scientists and public health officials. Notwithstanding, these species and others including Plasmodium coatneyi have served for decades as sources of knowledge on the biology, genetics and evolution of Plasmodium, and the diverse ramifications and outcomes of malaria in their monkey hosts. Experimental analysis of these species can help to fill gaps in knowledge beyond what may be possible studying the human malaria parasites or rodent parasite species. The genome sequences for these simian malaria parasite species were reported during the last decade, and functional genomics research has since been pursued. Here research on the functional genomics analysis involving these species is summarized and their importance is stressed, particularly for understanding host–parasite interactions, and potentially testing novel interventions. Importantly, while Plasmodium falciparum and Plasmodium vivax can be studied in small New World monkeys, the simian malaria parasites can be studied more effectively in the larger Old World monkey macaque hosts, which are more closely related to humans. In addition to ex vivo analyses, experimental scenarios can include passage through Anopheline mosquito hosts and longitudinal infections in monkeys to study acute and chronic infections, as well as relapses, all in the context of the in vivo host environment. Such experiments provide opportunities for understanding functional genomic elements that govern host–parasite interactions, immunity and pathogenesis in-depth, addressing hypotheses not possible from in vitro cultures or cross-sectional clinical studies with humans.

An Epidemiological Model of Malaria Accounting for Asymptomatic Carriers

Asymptomatic individuals in the context of malarial disease are subjects who carry a parasite load, but do not show clinical symptoms. A correct understanding of the influence of asymptomatic individuals on transmission dynamics will provide a comprehensive description of the complex interplay between the definitive host (female Anopheles mosquito), intermediate host (human), and agent (Plasmodium parasite). The goal of this article is to conduct a rigorous mathematical analysis of a new compartmentalized malaria model accounting for asymptomatic human hosts for the purpose of calculating the basic reproductive number ([Formula: see text]) and determining the bifurcations that might occur at the onset of disease-free equilibrium. A point of departure of this model from others appearing in the literature is that the asymptomatic compartment is decomposed into two mutually disjoint sub-compartments by making use of the naturally acquired immunity of the population under consideration. After deriving the model, a qualitative analysis is carried out to classify the stability of the equilibria of the system. Our results show that the dynamical system is locally asymptotically stable provided that [Formula: see text]. However, this stability is not global, owning to the occurrence of a sub-critical bifurcation in which additional non-trivial sub-threshold equilibrium solutions appear in response to a specified parameter being perturbed. To ensure that the model does not undergo a backward bifurcation, we demand an auxiliary parameter denoted [Formula: see text] in addition to the threshold constraint [Formula: see text]. The authors hope that this qualitative analysis will fill in the gaps of what is currently known about asymptomatic malaria and aid in designing strategies that assist the further development of malaria control and eradication efforts.

Multi-scale dynamics of infectious diseases

To address the challenge of multiscale dynamics of infectious diseases, the Mathematical Biosciences Institute organized a workshop at The Ohio State University to bring together scientists from a variety of disciplines to share expertise gained through looking at infectious diseases across different scales. The researchers at the workshop, held in April 2018, were specifically looking at three model systems: foot-and-mouth disease, vector-borne diseases and enteric diseases. Although every multiscale model must be necessarily derived from a multiscale system, not every multiscale system has to lead to multiscale models. These three model systems seem to have produced a variety of both multiscale and integrated single-scale mechanistic models that have developed their own strengths and particular challenges. Here, we present papers from some of the workshop participants to show the breadth of the field.

Risk alleles for tuberculosis infection associate with reduced immune reactivity in a wild mammalian host

Integrating biological processes across scales remains a central challenge in disease ecology. Genetic variation drives differences in host immune responses, which, along with environmental factors, generates temporal and spatial infection patterns in natural populations that epidemiologists seek to predict and control. However, genetics and immunology are typically studied in model systems, whereas population-level patterns of infection status and susceptibility are uniquely observable in nature. Despite obvious causal connections, organizational scales from genes to host outcomes to population patterns are rarely linked explicitly. Here we identify two loci near genes involved in macrophage (phagocyte) activation and pathogen degradation that additively increase risk of bovine tuberculosis infection by up to ninefold in wild African buffalo. Furthermore, we observe genotype-specific variation in IL-12 production indicative of variation in macrophage activation. Here, we provide measurable differences in infection resistance at multiple scales by characterizing the genetic and inflammatory variation driving patterns of infection in a wild mammal.

Coupling multiscale within-host dynamics and between-host transmission with recovery (SIR) dynamics

Multiscale models that link within-host infection to between-host transmission are valuable tools to progress understanding of viral infectious diseases. In this paper, we present two multiscale models that couple within-host infection to a susceptible-infected-recovered (SIR) model. A disease-induced transmission rate bridges the scales from within to between-host. Our stability analysis on the first model (influenza infection) reveals two equilibrium points for the SIR model that describe endemic scenarios where both susceptible and infected cases maintain nonzero population sizes. Consequently, the between-host system has two bifurcations determined by the corresponding basic reproduction number of the within-host and the size of the infected population at the interior equilibrium point. Analysis on the second model (Ebola infection) reveals the limited transient inhibitory effect of antibodies on viral replication, which influences the time window from infection to a potential outbreak. Simulations numerically illustrate our results.

Systems Biology-Based Investigation of Host-Plasmodium Interactions

Malaria is a serious, complex disease caused by parasites of the genus Plasmodium. Plasmodium parasites affect multiple tissues as they evade immune responses, replicate, sexually reproduce, and transmit between vertebrate and invertebrate hosts. The explosion of omics technologies has enabled large-scale collection of Plasmodium infection data, revealing systems-scale patterns, mechanisms of pathogenesis, and the ways that host and pathogen affect each other. Here, we provide an overview of recent efforts using systems biology approaches to study host-Plasmodium interactions and the biological themes that have emerged from these efforts. We discuss some of the challenges in using systems biology for this goal, key research efforts needed to address those issues, and promising future malaria applications of systems biology.

Multiscale model within-host and between-host for viral infectious diseases

Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes viral replication and the respective immune response while disease transmission is represented by a susceptible-infected model. The bridging of scales from within- to between-host considered transmission as a function of the viral load. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers [Formula: see text] and [Formula: see text] for the within- and the between-host subsystems, respectively. Local stability results for each subsystem, including a unique stable equilibrium point, recapitulate classical approaches to infection and epidemic control. Using a Lyapunov function, global stability of the between-host system was obtained. Our main result was the derivation of the [Formula: see text] as an increasing function of [Formula: see text]. Numerical analyses reveal that a Michaelis-Menten form based on the virus is more likely to recapitulate the behavior between the scales than a form directly proportional to the virus. Our work contributes basic understandings of the two models and casts light on the potential effects of the coupling function on linking the two scales.

Micro-epidemiology of mixed-species malaria infections in a rural population living in the Colombian Amazon region

Malaria outbreaks have been reported in recent years in the Colombian Amazon region, malaria has been re-emerging in areas where it was previously controlled. Information from malaria transmission networks and knowledge about the population characteristics influencing the dispersal of parasite species is limited. This study aimed to determine the distribution patterns of Plasmodium vivax, P. malariae and P. falciparum single and mixed infections, as well as the significant socio-spatial groupings relating to the appearance of such infections. An active search in 57 localities resulted in 2,106 symptomatic patients being enrolled. Parasitaemia levels were assessed by optical microscopy, and parasites were detected by PCR. The association between mixed infections (in 43.2% of the population) and socio-spatial factors was modelled using logistic regression and multiple correspondence analyses. P. vivax occurred most frequently (71.0%), followed by P. malariae (43.2%), in all localities. The results suggest that a parasite density-dependent regulation model (with fever playing a central role) was appropriate for modelling the frequency of mixed species infections in this population. This study highlights the under-reporting of Plasmodium spp. mixed infections in the malaria-endemic area of the Colombian Amazon region and the association between causative and environmental factors in such areas.

A complete categorization of multiscale models of infectious disease systems

Modelling of infectious disease systems has entered a new era in which disease modellers are increasingly turning to multiscale modelling to extend traditional modelling frameworks into new application areas and to achieve higher levels of detail and accuracy in characterizing infectious disease systems. In this paper we present a categorization framework for categorizing multiscale models of infectious disease systems. The categorization framework consists of five integration frameworks and five criteria. We use the categorization framework to give a complete categorization of host-level immuno-epidemiological models (HL-IEMs). This categorization framework is also shown to be applicable in categorizing other types of multiscale models of infectious diseases beyond HL-IEMs through modifying the initial categorization framework presented in this study. Categorization of multiscale models of infectious disease systems in this way is useful in bringing some order to the discussion on the structure of these multiscale models.

Metabolic modeling helps interpret transcriptomic changes during malaria

Disease represents a specific case of malfunctioning within a complex system. Whereas it is often feasible to observe and possibly treat the symptoms of a disease, it is much more challenging to identify and characterize its molecular root causes. Even in infectious diseases that are caused by a known parasite, it is often impossible to pinpoint exactly which molecular profiles of components or processes are directly or indirectly altered. However, a deep understanding of such profiles is a prerequisite for rational, efficacious treatments. Modern omics methodologies are permitting large-scale scans of some molecular profiles, but these scans often yield results that are not intuitive and difficult to interpret. For instance, the comparison of healthy and diseased transcriptome profiles may point to certain sets of involved genes, but a host of post-transcriptional processes and regulatory mechanisms renders predictions regarding metabolic or physiological consequences of the observed changes in gene expression unreliable. Here we present proof of concept that dynamic models of metabolic pathway systems may offer a tool for interpreting transcriptomic profiles measured during disease. We illustrate this strategy with the interpretation of expression data of genes coding for enzymes associated with purine metabolism. These data were obtained during infections of rhesus macaques (Macaca mulatta) with the malaria parasite Plasmodium cynomolgi or P. coatneyi. The model-based interpretation reveals clear patterns of flux redistribution within the purine pathway that are consistent between the two malaria pathogens and are even reflected in data from humans infected with P. falciparum. This article is part of a Special Issue entitled: Accelerating Precision Medicine through Genetic and Genomic Big Data Analysis edited by Yudong Cai & Tao Huang.

A model of Plasmodium vivax concealment based on Plasmodium cynomolgi infections in Macaca mulatta

BACKGROUND

Plasmodium vivax can cause severe malaria. The total parasite biomass during infections is correlated with the severity of disease but not necessarily quantified accurately by microscopy. This finding has raised the question whether there could be sub-populations of parasites that are not observed in peripheral blood smears but continue to contribute to the increase in parasite numbers that drive pathogenesis. Non-human primate infection models utilizing the closely related simian malaria parasite Plasmodium cynomolgi hold the potential for quantifying the magnitude of possibly unobserved infected red blood cell (iRBC) populations and determining how the presence of this hidden reservoir correlates with disease severity.

METHODS

Time series data tracking the longitudinal development of parasitaemia in five Macaca mulatta infected with P. cynomolgi were used to design a computational model quantifying iRBCs that circulate in the blood versus those that are not detectable and are termed here as 'concealed'. This terminology is proposed to distinguish such observations from the deep vascular and widespread 'sequestration' of Plasmodium falciparum iRBCs, which is governed by distinctly different molecular mechanisms.

RESULTS

The computational model presented here clearly demonstrates that the observed growth data of iRBC populations are not consistent with the known biology and blood-stage cycle of P. cynomolgi. However, the discrepancies can be resolved when a sub-population of concealed iRBCs is taken into account. The model suggests that the early growth of a hidden parasite sub-population has the potential to drive disease. As an alternative, the data could be explained by the sequential release of merozoites from the liver over a number of days, but this scenario seems less likely.

CONCLUSIONS

Concealment of a non-circulating iRBC sub-population during P. cynomolgi infection of M. mulatta is an important aspect of this successful host-pathogen relationship. The data also support the likelihood that a sub-population of iRBCs of P. vivax has a comparable means to become withdrawn from the peripheral circulation. This inference has implications for understanding vivax biology and pathogenesis and stresses the importance of considering a concealed parasite reservoir with regard to vivax epidemiology and the quantification and treatment of P. vivax infections.

Dendritic Cells and Leishmania Infection: Adding Layers of Complexity to a Complex Disease

Leishmaniasis is a group of neglected diseases whose clinical manifestations depend on factors from the host and the pathogen. It is an important public health problem worldwide caused by the protozoan parasite from the Leishmania genus. Cutaneous Leishmaniasis (CL) is the most frequent form of this disease transmitted by the bite of an infected sandfly into the host skin. The parasites can be uptook and/or recognized by macrophages, neutrophils, and/or dendritic cells (DCs). Initially, DCs were described to play a protective role in activating the immune response against Leishmania parasites. However, several reports showed a dichotomic role of DCs in modulating the host immune response to susceptibility or resistance in CL. In this review, we discuss (1) the interactions between DCs and parasites from different species of Leishmania and (2) the crosstalk of DCs and other cells during CL infection. The complexity of these interactions profoundly affects the adaptive immune response and, consequently, the disease outcome, especially from Leishmania species of the New World.

Comparison of mathematical frameworks for modeling erythropoiesis in the context of malaria infection

Malaria is an infectious disease present all around the globe and responsible for half a million deaths per year. A within-host model of this infection requires a framework capable of properly approximating not only the blood stage of the infection but also the erythropoietic process that is in charge of overcoming the malaria induced anemia. Within this context, we compare ordinary differential equations (ODEs) with and without age classes, delayed differential equations (DDEs), and discrete recursive equations (DREs) with age classes. Results show that ODEs without age classes are fair approximations that do not provide a crisp temporal representation of the processes involved, and inclusion of age classes only mitigates the problem to some degree. DDEs perform well with respect to generating the essentially fixed delay between cell production and cell removal due to age, but the inclusion of any other processes, such as sudden blood loss, becomes cumbersome. The framework that was found to perform best in representing the dynamics of red blood cells during malaria infection is a DRE with age classes. In this model structure, the amount of time a cell remains alive is easily controlled, and the addition of age dependent or independent processes is straightforward. All events that populations of cells face during their lifespan, like growth or adaptation in differentiation or maturation rate, are properly represented in this framework.