Mathematical Models Of Disease Transmission Research Articles

Spatial distribution of poultry farms using point pattern modelling: A method to address livestock environmental impacts and disease transmission risks.

The distribution of farm locations and sizes is paramount to characterize patterns of disease spread. With some regions undergoing rapid intensification of livestock production, resulting in increased clustering of farms in peri-urban areas, measuring changes in the spatial distribution of farms is crucial to design effective interventions. However, those data are not available in many countries, their generation being resource-intensive. Here, we develop a farm distribution model (FDM), which allows the prediction of locations and sizes of poultry farms in countries with scarce data. The model combines (i) a Log-Gaussian Cox process model to simulate the farm distribution as a spatial Poisson point process, and (ii) a random forest model to simulate farm sizes (i.e. the number of animals per farm). Spatial predictors were used to calibrate the FDM on intensive broiler and layer farm distributions in Bangladesh, Gujarat (Indian state) and Thailand. The FDM yielded realistic farm distributions in terms of spatial clustering, farm locations and sizes, while providing insights on the factors influencing these distributions. Finally, we illustrate the relevance of modelling realistic farm distributions in the context of epidemic spread by simulating pathogen transmission on an array of spatial distributions of farms. We found that farm distributions generated from the FDM yielded spreading patterns consistent with simulations using observed data, while random point patterns underestimated the probability of large outbreaks. Indeed, spatial clustering increases vulnerability to epidemics, highlighting the need to account for it in epidemiological modelling studies. As the FDM maintains a realistic distribution of farm location and sizes, its use to inform mathematical models of disease transmission is particularly relevant for regions where these data are not available.

Value of information analysis for pandemic response: intensive care unit preparedness at the onset of COVID-19

BackgroundDuring the early stages of the COVID-19 pandemic, there was considerable uncertainty surrounding epidemiological and clinical aspects of SARS-CoV-2. Governments around the world, starting from varying levels of pandemic preparedness, needed to make decisions about how to respond to SARS-CoV-2 with only limited information about transmission rates, disease severity and the likely effectiveness of public health interventions. In the face of such uncertainties, formal approaches to quantifying the value of information can help decision makers to prioritise research efforts.MethodsIn this study we use Value of Information (VoI) analysis to quantify the likely benefit associated with reducing three key uncertainties present in the early stages of the COVID-19 pandemic: the basic reproduction number (R_0), case severity (CS), and the relative infectiousness of children compared to adults (CI). The specific decision problem we consider is the optimal level of investment in intensive care unit (ICU) beds. Our analysis incorporates mathematical models of disease transmission and clinical pathways in order to estimate ICU demand and disease outcomes across a range of scenarios.ResultsWe found that VoI analysis enabled us to estimate the relative benefit of resolving different uncertainties about epidemiological and clinical aspects of SARS-CoV-2. Given the initial beliefs of an expert, obtaining more information about case severity had the highest parameter value of information, followed by the basic reproduction number R_0. Resolving uncertainty about the relative infectiousness of children did not affect the decision about the number of ICU beds to be purchased for any COVID-19 outbreak scenarios defined by these three parameters.ConclusionFor the scenarios where the value of information was high enough to justify monitoring, if CS and R_0 are known, management actions will not change when we learn about child infectiousness. VoI is an important tool for understanding the importance of each disease factor during outbreak preparedness and can help to prioritise the allocation of resources for relevant information.

Backward Bifurcation and Hysteresis in a Mathematical Model of COVID19 with Imperfect Vaccine

Vaccination has been used as strategy to eradicate the spread of COVID-19. But imperfect vaccine has been reported to induce backward bifurcation and hysteresis in mathematical models of disease transmission. Backward bifurcation is a phenomenon whereby a stable endemic equilibrium exists contemporaneously with a stable disease-free equilibrium when the basic reproduction number is less than 1. This situation can cause difficulty in controlling an epidemic because the basic reproduction is no longer the only means of eradicating the disease. In this paper, we propose a mathematical model for the transmission of disease which includes imperfect vaccination. We show that our model is capable of capturing backward bifurcation under certain conditions. By using parameters that are relevant to COVID-19 transmission in Malaysia, our numerical analysis shows that low vaccine efficacy can trigger backward bifurcation.

Test-trace-isolate-quarantine (TTIQ) intervention strategies after symptomatic COVID-19 case identification.

The test-trace-isolate-quarantine (TTIQ) strategy, where confirmed-positive pathogen carriers are isolated from the community and their recent close contacts are identified and pre-emptively quarantined, is used to break chains of transmission during a disease outbreak. The protocol is frequently followed after an individual presents with disease symptoms, at which point they will be tested for the pathogen. This TTIQ strategy, along with hygiene and social distancing measures, make up the non-pharmaceutical interventions that are utilised to suppress the ongoing COVID-19 pandemic. Here we develop a tractable mathematical model of disease transmission and the TTIQ intervention to quantify how the probability of detecting and isolating a case following symptom onset, the fraction of contacts that are identified and quarantined, and the delays inherent to these processes impact epidemic growth. In the model, the timing of disease transmission and symptom onset, as well as the frequency of asymptomatic cases, is based on empirical distributions of SARS-CoV-2 infection dynamics, while the isolation of confirmed cases and quarantine of their contacts is implemented by truncating their respective infectious periods. We find that a successful TTIQ strategy requires intensive testing: the majority of transmission is prevented by isolating symptomatic individuals and doing so in a short amount of time. Despite the lesser impact, additional contact tracing and quarantine increases the parameter space in which an epidemic is controllable and is necessary to control epidemics with a high reproductive number. TTIQ could remain an important intervention for the foreseeable future of the COVID-19 pandemic due to slow vaccine rollout and highly-transmissible variants with the potential for vaccine escape. Our results can be used to assess how TTIQ can be improved and optimised, and the methodology represents an improvement over previous quantification methods that is applicable to future epidemic scenarios.

Communicating uncertainty in epidemic models

While mathematical models of disease transmission are widely used to inform public health decision-makers globally, the uncertainty inherent in results are often poorly communicated. We outline some potential sources of uncertainty in epidemic models, present traditional methods used to illustrate uncertainty and discuss alternative presentation formats used by modelling groups throughout the COVID-19 pandemic. Then, by drawing on the experience of our own recent modelling, we seek to contribute to the ongoing discussion of how to improve upon traditional methods used to visualise uncertainty by providing a suggestion of how this can be presented in a clear and simple manner.

Quantifying heterogeneity in SARS-CoV-2 transmission during the lockdown in India

The novel SARS-CoV-2 virus, as it manifested in India in April 2020, showed marked heterogeneity in its transmission. Here, we used data collected from contact tracing during the lockdown in response to the first wave of COVID-19 in Punjab, a major state in India, to quantify this heterogeneity, and to examine implications for transmission dynamics. We found evidence of heterogeneity acting at multiple levels: in the number of potentially infectious contacts per index case, and in the per-contact risk of infection. Incorporating these findings in simple mathematical models of disease transmission reveals that these heterogeneities act in combination to strongly influence transmission dynamics. Standard approaches, such as representing heterogeneity through secondary case distributions, could be biased by neglecting these underlying interactions between heterogeneities. We discuss implications for policy, and for more efficient contact tracing in resource-constrained settings such as India. Our results highlight how contact tracing, an important public health measure, can also provide important insights into epidemic spread and control.

Comparing metapopulation dynamics of infectious diseases under different models of human movement

Newly available datasets present exciting opportunities to investigate how human population movement contributes to the spread of infectious diseases across large geographical distances. It is now possible to construct realistic models of infectious disease dynamics for the purposes of understanding global-scale epidemics. Nevertheless, a remaining unanswered question is how best to leverage the new data to parameterize models of movement, and whether one's choice of movement model impacts modeled disease outcomes. We adapt three well-studied models of infectious disease dynamics, the susceptible-infected-recovered model, the susceptible-infected-susceptible model, and the Ross-Macdonald model, to incorporate either of two candidate movement models. We describe the effect that the choice of movement model has on each disease model's results, finding that in all cases, there are parameter regimes where choosing one movement model instead of another has a profound impact on epidemiological outcomes. We further demonstrate the importance of choosing an appropriate movement model using the applied case of malaria transmission and importation on Bioko Island, Equatorial Guinea, finding that one model produces intelligible predictions of R 0, whereas the other produces nonsensical results.

Quantifying the risk of vector-borne disease transmission attributable to genetically modified vectors.

The relative risk of disease transmission caused by the potential release of transgenic vectors, such as through sterile insect technique or gene drive systems, is assessed with comparison with wild-type vectors. The probabilistic risk framework is demonstrated with an assessment of the relative risk of lymphatic filariasis, malaria and o'nyong'nyong arbovirus transmission by mosquito vectors to human hosts given a released transgenic strain of Anopheles coluzzii carrying a dominant sterile male gene construct. Harm is quantified by a logarithmic loss function that depends on the causal risk ratio, which is a quotient of basic reproduction numbers derived from mathematical models of disease transmission. The basic reproduction numbers are predicted to depend on the number of generations in an insectary colony and the number of backcrosses between the transgenic and wild-type lineages. Analogous causal risk ratios for short-term exposure to a single cohort release are also derived. These causal risk ratios were parametrized by probabilistic elicitations, and updated with experimental data for adult vector mortality. For the wild-type, high numbers of insectary generations were predicted to reduce the number of infectious human cases compared with uncolonized wild-type. Transgenic strains were predicted to produce fewer infectious cases compared with the uncolonized wild-type.

Estimating epidemiological parameters using diagnostic testing data from low pathogenicity avian influenza infected turkey houses

Limiting spread of low pathogenicity avian influenza (LPAI) during an outbreak is critical to reduce the negative impact on poultry producers and local economies. Mathematical models of disease transmission can support outbreak control efforts by estimating relevant epidemiological parameters. In this article, diagnostic testing data from each house on a premises infected during a LPAI H5N2 outbreak in the state of Minnesota in the United States in 2018 was used to estimate the time of virus introduction and adequate contact rate, which determines the rate of disease spread. A well-defined most likely time of virus introduction, and upper and lower 95% credibility intervals were estimated for each house. The length of the 95% credibility intervals ranged from 11 to 22 with a mean of 17 days. In some houses the contact rate estimates were also well-defined; however, the estimated upper 95% credibility interval bound for the contact rate was occasionally dependent on the upper bound of the prior distribution. The estimated modes ranged from 0.5 to 6.0 with a mean of 2.8 contacts per day. These estimates can be improved with early detection, increased testing of monitored premises, and combining the results of multiple barns that possess similar production systems.

A coadunation of biological and mathematical perspectives on the pandemic COVID-19: A Review

Background: Coronavirus disease 2019 (COVID-19) outbreak has created an emergency globally, and social distancing and isolation is the only solution to prevent its spread. Several countries have announced full lockdown to tackle this pandemic. The coronavirus family is inclusive of pathogens of both – animal species and humans, encapsulating the isolated severe acute respiratory syndrome coronavirus (SARS-CoV). Researchers round the globe have been dexterously working to decode this lethal virus. Many mathematical frameworks have also been depicted which have helped to understand the dynamics of the COVID-19. Methods: This systematic review highlights the virus genomic composition, preliminary phylogenetic analysis, pathogenesis, symptomatology, diagnosis, and prognosis along with mathematical models of disease transmission and dynamics. Results: Our preliminary phylogenetic analysis of the novel coronavirus sequence discerns that although shares its lineage with SARS, BAT-CoV, Beta-BAT-SARS,however, this protein is highly dissimilar to its ancestors. The widely prominent amino acid residues found in the protein are alanine (ALA), aspartic acid (ASP), phenylalanine (PHE), leucine (LEU), aspartic acid (ASP), threonine (THR), valine (VAL), tyrosine (TYR) and asparagine (ASN) that are responsible for its replication process. Conclusion: Research on coronaviruses continues towards developing a strong understanding of the rapidly evolving viral replication and its transmission between individuals.

A generalized differential equation compartmental model of infectious disease transmission.

For decades, mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression, control, and prevention of disease spread. Of these models, one of the most fundamental is the SIR differential equation model. However, this ubiquitous model has one significant and rarely acknowledged shortcoming: it is unable to account for a disease's true infectious period distribution. As the misspecification of such a biological characteristic is known to significantly affect model behavior, there is a need to develop new modeling approaches that capture such information. Therefore, we illustrate an innovative take on compartmental models, derived from their general formulation as systems of nonlinear Volterra integral equations, to capture a broader range of infectious period distributions, yet maintain the desirable formulation as systems of differential equations. Our work illustrates a compartmental model that captures any Erlang distributed duration of infection with only 3 differential equations, instead of the typical inflated model sizes required by traditional differential equation compartmental models, and a compartmental model that captures any mean, standard deviation, skewness, and kurtosis of an infectious period distribution with 4 differential equations. The significance of our work is that it opens up a new class of easy-to-use compartmental models to predict disease outbreaks that do not require a complete overhaul of existing theory, and thus provides a starting point for multiple research avenues of investigation under the contexts of mathematics, public health, and evolutionary biology.

Development of Compartmental Mathematical Model of Disease Transmission of Basal Stem Rot in Oil Palm Plantation

The mathematical modelling is one of the major research areas for mathematician and biologist in understanding the dynamics of transmissible infections. There might also be a mathematical model used to research the dynamics of plant disease and estimate the number of cases of outbreaks. In this research, we developed the compartmental mathematical model of the dynamical spread of transmission of plant disease with reference to basal stem rot (BSR) disease in oil palm plantation. The dynamics of the BSR disease were studied by a prone-contagious-sustained (PCS) compartmental mathematical model involving ordinary differential equations for three classes of hosts; prone, contagious and sustained. The equilibrium points and epidemic threshold conditions were analytically determined and numerical simulations were analyzed to support analytical results. From the numerical results, the solutions converge to each equilibrium state and PCS model simulation indicated that BSR disease has not become endemic. In particular, the threshold parameters that summarize the dynamics of the system will help to choose strategies for crop protection.

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

The observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: within-host, that is, how an infection progresses inside a single individual (for instance viral and immune dynamics), and between-host, that is, how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a holistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission (as defined by combining within-host and between-host scales) to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 24 of 197 qualifying papers across 30 years that include both linked models at the within and between host scales and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.

Using Contact Patterns to Inform HIV Interventions in Persons Who Inject Drugs in Northern Vietnam.

Population mixing patterns can greatly inform allocation of HIV prevention interventions such as treatment as prevention or preexposure prophylaxis. Characterizing contact patterns among subgroups can help identify the specific combinations of contact expected to result in the greatest number of new infections. Baseline data from an intervention to reduce HIV-related risk behaviors in male persons who inject drugs (PWID) in the Northern Vietnamese province of Thai Nguyen were used for the analysis. Egocentric network data were provided by PWID who reported any drug-injection equipment sharing in the previous 3 months. Age-dependent mixing was assessed to explore its epidemiological implications on risk of HIV transmission risk (among those HIV-infected) and HIV acquisition risk (among those not infected) in PWID. A total of 1139 PWID collectively reported 2070 equipment-sharing partnerships in the previous 3 months. Mixing by age identified the 30-34 and 35-39 years age groups as the groups from whom the largest number of new infections was transmitted, making them primary targets for treatment as prevention. Among the uninfected, 25-29, 30-35, and 35-39 years age groups had the highest HIV acquisition rate, making them the primary targets for preexposure prophylaxis. Collection and analysis of contact patterns in PWID is feasible and can greatly inform infectious disease dynamics and targeting of appropriate interventions. Results presented also provide much needed empirical data on mixing to improve mathematical models of disease transmission in this population.

Epidemix—An interactive multi-model application for teaching and visualizing infectious disease transmission

Mathematical models of disease transmission are used to improve our understanding of patterns of infection and to identify factors influencing them. During recent public and animal health crises, such as pandemic influenza, Ebola, Zika, foot-and-mouth disease, models have made important contributions in addressing policy questions, especially through the assessment of the trajectory and scale of outbreaks, and the evaluation of control interventions. However, their mathematical formulation means that they may appear as a “black box” to those without the appropriate mathematical background. This may lead to a negative perception of their utility for guiding policy, and generate expectations, which are not in line with what these models can deliver. It is therefore important for policymakers, as well as public health and animal health professionals and researchers who collaborate with modelers and use results generated by these models for policy development or research purpose, to understand the key concepts and assumptions underlying these models.The software application epidemix (http://shinyapps.rvc.ac.uk) presented here aims to make mathematical models of disease transmission accessible to a wider audience of users. By developing a visual interface for a suite of eight models, users can develop an understanding of the impact of various modelling assumptions – especially mixing patterns – on the trajectory of an epidemic and the impact of control interventions, without having to directly deal with the complexity of mathematical equations and programming languages. Models are compartmental or individual-based, deterministic or stochastic, and assume homogeneous or heterogeneous-mixing patterns (with the probability of transmission depending on the underlying structure of contact networks, or the spatial distribution of hosts). This application is intended to be used by scientists teaching mathematical modelling short courses to non-specialists – including policy makers, public and animal health professionals and students – and wishing to develop hands-on practicals illustrating key concepts of disease dynamics and control.

Mathematical models of infection transmission in healthcare settings: recent advances from the use of network structured data.

Mathematical modeling approaches have brought important contributions to the study of pathogen spread in healthcare settings over the last 20 years. Here, we conduct a comprehensive systematic review of mathematical models of disease transmission in healthcare settings and assess the application of contact and patient transfer network data over time and their impact on our understanding of transmission dynamics of infections. Recently, with the increasing availability of data on the structure of interindividual and interinstitution networks, models incorporating this type of information have been proposed, with the aim of providing more realistic predictions of disease transmission in healthcare settings. Models incorporating realistic data on individual or facility networks often remain limited to a few settings and a few pathogens (mostly methicillin-resistant Staphylococcus aureus). To respond to the objectives of creating improved infection prevention and control measures and better understanding of healthcare-associated infections transmission dynamics, further innovations in data collection and parameter estimation in modeling is required.

Defining the population attributable fraction for infectious diseases.

The population attributable fraction (PAF) is used to quantify the contribution of a risk group to disease burden. For infectious diseases, high-risk individuals may increase disease risk for the wider population in addition to themselves; therefore methods are required to estimate the PAF for infectious diseases. A mathematical model of disease transmission in a population with a high-risk group was used to compare existing approaches for calculating the PAF. We quantify when existing methods are consistent and when estimates diverge. We introduce a new method, based on the basic reproduction number, for calculating the PAF, which bridges the gap between existing methods and addresses shortcomings. We illustrate the methods with two examples of the contribution of badgers to bovine tuberculosis in cattle and the role of commercial sex in an HIV epidemic. We demonstrate that current methods result in irreconcilable PAF estimates, depending on how chains of transmission are categorized. Using two novel simple formulae for emerging and endemic diseases, we demonstrate that the largest differences occur when transmission in the general population is not self-sustaining. Crucially, some existing methods are not able to discriminate between multiple risk groups. We show that compared with traditional estimates, assortative mixing leads to a decreased PAF, whereas disassortative mixing increases PAF. Recent methods for calculating the population attributable fraction (PAF) are not consistent with traditional approaches. Policy makers and users of PAF statistics should be aware of these differences. Our approach offers a straightforward and parsimonious method for calculating the PAF for infectious diseases.

Social contacts, vaccination decisions and influenza in Japan

BackgroundContact patterns and vaccination decisions are fundamental to transmission dynamics of infectious diseases. We report on age-specific contact patterns in Japan and their effect on influenza vaccination behaviour.MethodsJapanese adults (N=3146)...

Epidemic cycles driven by host behaviour.

Host immunity and demographics (the recruitment of susceptibles via birthrate) have been demonstrated to be a key determinant of the periodicity of measles, pertussis and dengue epidemics. However, not all epidemic cycles are from pathogens inducing sterilizing immunity or are driven by demographics. Many sexually transmitted infections are driven by sexual behaviour. We present a mathematical model of disease transmission where individuals can disconnect and reconnect depending on the infectious status of their contacts. We fit the model to historic syphilis (Treponema pallidum) and gonorrhea (Neisseria gonorrhoeae) incidence in the USA and explore potential intervention strategies against syphilis. We find that cycles in syphilis incidence can be driven solely by changing sexual behaviour in structured populations. Our model also explains the lack of similar cycles in gonorrhea incidence even if the two infections share the same propagation pathways. Our model similarly illustrates how sudden epidemic outbreaks can occur on time scales smaller than the characteristic demographic time scale of the population and that weaker infections can lead to more violent outbreaks. Behaviour also appears to be critical for control strategies as we found a bigger sensitivity to behavioural interventions than antibiotic treatment. Thus, behavioural interventions may play a larger role than previously thought, especially in the face of antibiotic resistance and low intervention efficacies.

Assessment of pertussis vaccination strategies using a mathematical model of disease transmission

Pertussis or whooping cough is a vaccine-preventable respiratory disease that has reemerged in the past decades. A higher morbidity and mortality has been recorded in infants, although cases have also been reported in adolescents and adults. The epidemiological scenario for this condition has urged to review and implement new strategies aimed at improving its control. However, many of these strategies have not been investigated in depth so as to be established as universal. In this context, mathematical models of disease transmission are useful decision-making tools. Using a mathematical model of pertussis, this study assessed the possible impact of the different control measures on the most vulnerable population (0-1 year old infants). In particular, the analysis focused on the impact of including a booster vaccination at 11 years old, the effect of improving the coverage provided by primary doses, and the reduction of any delay in their administration. The assessment also estimated the effect of immunizing pregnant women. Results show that including a booster dose at 11 years reduces the incidence of pertussis by 3% in infants younger than 1 year old. In addition, administering primary doses in compliance with the schedule (with no delays) reduces pertussis incidence by 16%. Increasing coverage from 80% to 95% results in a signifcantly decreased incidence in the vulnerable population (38%). If the percentage of immunized pregnant women reaches 50%, the reduction of the most severe infant cases could be more than 43% (0-2 month-old infants).