Linked within-host and between-host models and data for infectious diseases: a systematic review

Trade-offs shaping transmission of sylvatic dengue and Zika viruses in monkey hosts

Mosquito-borne dengue (DENV) and Zika (ZIKV) viruses originated in Old World sylvatic (forest) cycles involving monkeys and canopy-living Aedes mosquitoes. Both viruses spilled over into human transmission and were translocated to the Americas, opening a path for spillback into Neotropical sylvatic cycles. Studies of the trade-offs that shape within-host dynamics and transmission of these viruses are lacking, hampering efforts to predict spillover and spillback. We infected a native, Asian host species (cynomolgus macaque) and a novel, American host species (squirrel monkey) with sylvatic strains of DENV-2 or ZIKV via mosquito bite. We then monitored aspects of viral replication (viremia), innate and adaptive immune response (natural killer (NK) cells and neutralizing antibodies, respectively), and transmission to mosquitoes. In both hosts, ZIKV reached high titers that translated into high transmission to mosquitoes; in contrast DENV-2 replicated to low levels and, unexpectedly, transmission occurred only when serum viremia was below or near the limit of detection. Our data reveal evidence of an immunologically-mediated trade-off between duration and magnitude of virus replication, as higher peak ZIKV titers are associated with shorter durations of viremia, and higher NK cell levels are associated with lower peak ZIKV titers and lower anti-DENV-2 antibody levels. Furthermore, patterns of transmission of each virus from a Neotropical monkey suggest that ZIKV has greater potential than DENV-2 to establish a sylvatic transmission cycle in the Americas.

Quantifying the relationship between within-host dynamics and transmission for viral diseases of livestock

Understanding the population dynamics of an infectious disease requires linking within-host dynamics and between-host transmission in a quantitative manner, but this is seldom done in practice. Here a simple phenomenological model for viral dynamics within a host is linked to between-host transmission by assuming that the probability of transmission is related to log viral titre. Data from transmission experiments for two viral diseases of livestock, foot-and-mouth disease virus in cattle and swine influenza virus in pigs, are used to parametrize the model and, importantly, test the underlying assumptions. The model allows the relationship between within-host parameters and transmission to be determined explicitly through their influence on the reproduction number and generation time. Furthermore, these critical within-host parameters (time and level of peak titre, viral growth and clearance rates) can be computed from more complex within-host models, raising the possibility of assessing the impact of within-host processes on between-host transmission in a more detailed quantitative manner.

Mathematical methods for scaling from within-host to population-scale in infectious disease systems

Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.

Analysis of the risk and pre-emptive control of viral outbreaks accounting for within-host dynamics: SARS-CoV-2 as a case study

In the era of living with COVID-19, the risk of localised SARS-CoV-2 outbreaks remains. Here, we develop a multiscale modelling framework for estimating the local outbreak risk for a viral disease (the probability that a major outbreak results from a single case introduced into the population), accounting for within-host viral dynamics. Compared to population-level models previously used to estimate outbreak risks, our approach enables more detailed analysis of how the risk can be mitigated through pre-emptive interventions such as antigen testing. Considering SARS-CoV-2 as a case study, we quantify the within-host dynamics using data from individuals with omicron variant infections. We demonstrate that regular antigen testing reduces, but may not eliminate, the outbreak risk, depending on characteristics of local transmission. In our baseline analysis, daily antigen testing reduces the outbreak risk by 45% compared to a scenario without antigen testing. Additionally, we show that accounting for heterogeneity in within-host dynamics between individuals affects outbreak risk estimates and assessments of the impact of antigen testing. Our results therefore highlight important factors to consider when using multiscale models to design pre-emptive interventions against SARS-CoV-2 and other viruses.

An immuno-epidemiological model linking between-host and within-host dynamics of cholera

Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health, with a yearly estimated global burden of 2.9 million cases. Although most existing models for the disease focus on its population dynamics, the disease evolves from within-host processes to the population, making it imperative to link the multiple scales of the disease to gain better perspectives on its spread and control. In this study, we propose an immuno-epidemiological model that links the between-host and within-host dynamics of cholera. The immunological (within-host) model depicts the interaction of the cholera pathogen with the adaptive immune response. We distinguish pathogen dynamics from immune response dynamics by assigning different time scales. Through a time-scale analysis, we characterise a single infected person by their immune response. Contrary to other within-host models, this modelling approach allows for recovery through pathogen clearance after a finite time. Then, we scale up the dynamics of the infected person to construct an epidemic model, where the infected population is structured by individual immunological dynamics. We derive the basic reproduction number ($ \mathcal{R}_0 $) and analyse the stability of the equilibrium points. At the disease-free equilibrium, the disease will either be eradicated if $ \mathcal{R}_0 < 1 $ or otherwise persists. A unique endemic equilibrium exists when $ \mathcal{R}_0 > 1 $ and is locally asymptotically stable without a loss of immunity.

Immunologically mediated trade-offs shaping transmission of sylvatic dengue and Zika viruses in native and novel non-human primate hosts

Mosquito-borne dengue (DENV) and Zika (ZIKV) viruses originated in Old World sylvatic cycles involving monkey hosts, spilled over into human transmission, and were translocated to the Americas, creating potential for spillback into neotropical sylvatic cycles. Studies of the trade-offs that shape within-host dynamics and transmission of these viruses are lacking, hampering efforts to predict spillover and spillback. We exposed native (cynomolgus macaque) or novel (squirrel monkey) hosts to mosquitoes infected with either sylvatic DENV or ZIKV and monitored viremia, natural killer cells, transmission to mosquitoes, cytokines, and neutralizing antibody titers. Unexpectedly, DENV transmission from both host species occurred only when serum viremia was undetectable or near the limit of detection. ZIKV replicated in squirrel monkeys to much higher titers than DENV and was transmitted more efficiently but stimulated lower neutralizing antibody titers. Increasing ZIKV viremia led to greater instantaneous transmission and shorter duration of infection, consistent with a replication-clearance trade-off.

A Multiscale Model of COVID-19 Dynamics

COVID-19, caused by the infection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been a global pandemic and created unprecedented public health challenges throughout the world. Despite significant progresses in understanding the disease pathogenesis and progression, the epidemiological triad of pathogen, host, and environment remains unclear. In this paper, we develop a multiscale model to study the coupled within-host and between-host dynamics of COVID-19. The model includes multiple transmission routes (both human-to-human and environment-to-human) and connects multiple scales (both the population and individual levels). A detailed analysis on the local and global dynamics of the fast system, slow system and full system shows that rich dynamics, including both forward and backward bifurcations, emerge with the coupling of viral infection and epidemiological models. Model fitting to both virological and epidemiological data facilitates the evaluation of the influence of a few infection characteristics and antiviral treatment on the spread of the disease. Our work underlines the potential role that the environment can play in the transmission of COVID-19. Antiviral treatment of infected individuals can delay but cannot prevent the emergence of disease outbreaks. These results highlight the implementation of comprehensive intervention measures such as social distancing and wearing masks that aim to stop airborne transmission, combined with surface disinfection and hand hygiene that can prevent environmental transmission. The model also provides a multiscale modeling framework to study other infectious diseases when the environment can serve as a reservoir of pathogens.

Evaluating efficacy of indoor non-pharmaceutical interventions against COVID-19 outbreaks with a coupled spatial-SIR agent-based simulation framework

Contagious respiratory diseases, such as COVID-19, depend on sufficiently prolonged exposures for the successful transmission of the underlying pathogen. It is important that organizations evaluate the efficacy of non-pharmaceutical interventions aimed at mitigating viral transmission among their personnel. We have developed a operational risk assessment simulation framework that couples a spatial agent-based model of movement with an agent-based SIR model to assess the relative risks of different intervention strategies. By applying our model on MIT's Stata center, we assess the impacts of three possible dimensions of intervention: one-way vs unrestricted movement, population size allowed onsite, and frequency of leaving designated work location for breaks. We find that there is no significant impact made by one-way movement restrictions over unrestricted movement. Instead, we find that reducing the frequency at which individuals leave their workstations combined with lowering the number of individuals admitted below the current recommendations lowers the likelihood of highly connected individuals within the contact networks that emerge, which in turn lowers the overall risk of infection. We discover three classes of possible interventions based on their epidemiological effects. By assuming a direct relationship between data on secondary attack rates and transmissibility in the agent-based SIR model, we compare relative infection risk of four respiratory illnesses, MERS, SARS, COVID-19, and Measles, within the simulated area, and recommend appropriate intervention guidelines.

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.

The Use and Underuse of Model Systems in Infectious Disease Ecology and Evolutionary Biology

AbstractEver since biologists began studying the ecology and evolution of infectious diseases (EEID), laboratory-based model systems have been important for developing and testing theory. Yet what EEID researchers mean by the term "model systems" and what they want from them is unclear. This uncertainty hinders our ability to maximally exploit these systems, identify knowledge gaps, and establish effective new model systems. Here, we borrow a definition of model systems from the biomolecular sciences to assess how EEID researchers are (and are not) using 10 key model systems. According to this definition, model systems in EEID are not being used to their fullest and, in fact, cannot even be considered model systems. Research using these systems consistently addresses only two of the three fundamental processes that underlie disease dynamics-transmission and disease, but not recovery. Furthermore, studies tend to focus on only a few scales of biological organization that matter for disease ecology and evolution. Moreover, the field lacks an infrastructure to perform comparative analyses. We aim to begin a discussion of what we want from model systems, which would further progress toward a thorough, holistic understanding of EEID.

Mathematical modelling of Toxoplasma gondii transmission: A systematic review

BACKGROUND

Toxoplasma gondii is a ubiquitous protozoan parasite that can infect virtually all warm-blooded animals. It is the causative agent of toxoplasmosis, a significant public health issue worldwide. Mathematical models are useful to study the transmission dynamics of T. gondii infection in different settings, and may be used to compare the effectiveness of prevention measures.

METHODS

To obtain an overview of existing mathematical models for transmission of T. gondii, a systematic review was undertaken. The review was conducted according to an a priori protocol and the results were reported according to the PRISMA guidelines. Specific search terms were developed and used in the search of three databases (Scopus, PubMed, and Embase).

RESULTS

In total, 484 unique records were retrieved from the systematic search. Among them, 15 studies that used mathematical models to study the transmission of T. gondii. These studies were categorized into four groups based on the primary aims: dynamics of transmission (n = 8), intervention (n = 5), spatial distribution (n = 1), and outbreak investigation (n = 1).

CONCLUSIONS

Considering the high disease burden caused by T. gondii, the number of studies using mathematical models to understand the transmission dynamics of this parasite and to evaluate the effectiveness of intervention measures was only 15. This systematic review provides an overview of existing mathematical models and identifies the data gaps for model building. The results from this study can be helpful for further development of mathematical models and improved understanding of the transmission dynamics of T. gondii infection.

Cross-scale dynamics and the evolutionary emergence of infectious diseases

When emerging pathogens encounter new host species for which they are poorly adapted, they must evolve to escape extinction. Pathogens experience selection on traits at multiple scales, including replication rates within host individuals and transmissibility between hosts. We analyze a stochastic model linking pathogen growth and competition within individuals to transmission between individuals. Our analysis reveals a new factor, the cross-scale reproductive number of a mutant virion, that quantifies how quickly mutant strains increase in frequency when they initially appear in the infected host population. This cross-scale reproductive number combines with viral mutation rates, single-strain reproductive numbers, and transmission bottleneck width to determine the likelihood of evolutionary emergence, and whether evolution occurs swiftly or gradually within chains of transmission. We find that wider transmission bottlenecks facilitate emergence of pathogens with short-term infections, but hinder emergence of pathogens exhibiting cross-scale selective conflict and long-term infections. Our results provide a framework to advance the integration of laboratory, clinical, and field data in the context of evolutionary theory, laying the foundation for a new generation of evidence-based risk assessment of emergence threats.

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models.

The research and development process for multiscale models of infectious disease systems

Multiscale modelling of infectious disease systems falls within the domain of complexity science—the study of complex systems. However, what should be made clear is that current progress in multiscale modelling of infectious disease dynamics is still as yet insufficient to present it as a mature sub-discipline of complexity science. In this article we present a methodology for development of multiscale models of infectious disease systems. This methodology is a set of partially ordered research and development activities that result in multiscale models of infectious disease systems built from different scientific approaches. Therefore, the conclusive result of this article is a methodology to design multiscale models of infectious diseases. Although this research and development process for multiscale models cannot be claimed to be unique and final, it constitutes a good starting point, which may be found useful as a basis for further refinement in the discourse for multiscale modelling of infectious disease dynamics.

Complex systems such as infectious disease systems are inherently multilevel and multiscale systems. The study of such complex systems is called complexity science. In this article we present a methodology to design multiscale models of infectious disease systems from a complex systems perspective. Within this perspective we define complexity science as the study of the interconnected relationships of the levels and scales of organization of a complex system. We therefore, define the degree of complexity of a complex system as the number of levels and scales of organization of the complex system needed to describe it. In this work we first present a common multiscale vision of the multilevel and multiscale structure of infectious disease systems as complex systems in which the levels and scales of organization of an infectious disease system interact through different self-sustained multiscale cycles/loops (primary multiscale loops, or secondary multiscale loops, or tertiary multiscale loops) formed at different levels of organization of an infectious disease system due to ongoing reciprocal influence between the microscale and the macroscale. Guided by this multiscale vision, we propose a four-stage research and development process that result in multiscale models of infectious disease systems built from different scientific approaches.