Mathematical model of susceptibility, resistance, and resilience in the within-host dynamics between a Plasmodium parasite and the immune system

Uncovering the effects of heterogeneity and parameter sensitivity on within-host dynamics of disease: malaria as a case study

Background

The fidelity and reliability of disease model predictions depend on accurate and precise descriptions of processes and determination of parameters. Various models exist to describe within-host dynamics during malaria infection but there is a shortage of clinical data that can be used to quantitatively validate them and establish confidence in their predictions. In addition, model parameters often contain a degree of uncertainty and show variations between individuals, potentially undermining the reliability of model predictions. In this study models were reproduced and analysed by means of robustness, uncertainty, local sensitivity and local sensitivity robustness analysis to establish confidence in their predictions.

Results

Components of the immune system are responsible for the most uncertainty in model outputs, while disease associated variables showed the greatest sensitivity for these components. All models showed a comparable degree of robustness but displayed different ranges in their predictions. In these different ranges, sensitivities were well-preserved in three of the four models.

Conclusion

Analyses of the effects of parameter variations in models can provide a comparative tool for the evaluation of model predictions. In addition, it can assist in uncovering model weak points and, in the case of disease models, be used to identify possible points for therapeutic intervention.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04289-z.

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.

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

Since their earliest days, humans have been struggling with infectious diseases. Caused by viruses, bacteria, protozoa, or even higher organisms like worms, these diseases depend critically on numerous intricate interactions between parasites and hosts, and while we have learned much about these interactions, many details are still obscure. It is evident that the combined host-parasite dynamics constitutes a complex system that involves components and processes at multiple scales of time, space, and biological organization. At one end of this hierarchy we know of individual molecules that play crucial roles for the survival of a parasite or for the response and survival of its host. At the other end, one realizes that the spread of infectious diseases by far exceeds specific locales and, due to today's easy travel of hosts carrying a multitude of organisms, can quickly reach global proportions. The community of mathematical modelers has been addressing specific aspects of infectious diseases for a long time. Most of these efforts have focused on one or two select scales of a multi-level disease and used quite different computational approaches. This restriction to a molecular, physiological, or epidemiological level was prudent, as it has produced solid pillars of a foundation from which it might eventually be possible to launch comprehensive, multi-scale modeling efforts that make full use of the recent advances in biology and, in particular, the various high-throughput methodologies accompanying the emerging -omics revolution. This special issue contains contributions from biologists and modelers, most of whom presented and discussed their work at the workshop From within Host Dynamics to the Epidemiology of Infectious Disease, which was held at the Mathematical Biosciences Institute at Ohio State University in April 2014. These contributions highlight some of the forays into a deeper understanding of the dynamics between parasites and their hosts, and the consequences of this dynamics for the spread and treatment of infectious diseases.

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

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