COVID-19 vaccination strategies in Africa: A scoping review of the use of mathematical models to inform policy

OBJECTIVE

Mathematical models are vital tools to understand transmission dynamics and assess the impact of interventions to mitigate COVID-19. However, historically, their use in Africa has been limited. In this scoping review, we assess how mathematical models were used to study COVID-19 vaccination to potentially inform pandemic planning and response in Africa.

METHODS

We searched six electronic databases: MEDLINE, Embase, Web of Science, Global Health, MathSciNet and Africa-Wide NiPAD, using keywords to identify articles focused on the use of mathematical modelling studies of COVID-19 vaccination in Africa that were published as of October 2022. We extracted the details on the country, author affiliation, characteristics of models, policy intent and heterogeneity factors. We assessed quality using 21-point scale criteria on model characteristics and content of the studies.

RESULTS

The literature search yielded 462 articles, of which 32 were included based on the eligibility criteria. Nineteen (59%) studies had a first author affiliated with an African country. Of the 32 included studies, 30 (94%) were compartmental models. By country, most studies were about or included South Africa (n = 12, 37%), followed by Morocco (n = 6, 19%) and Ethiopia (n = 5, 16%). Most studies (n = 19, 59%) assessed the impact of increasing vaccination coverage on COVID-19 burden. Half (n = 16, 50%) had policy intent: prioritising or selecting interventions, pandemic planning and response, vaccine distribution and optimisation strategies and understanding transmission dynamics of COVID-19. Fourteen studies (44%) were of medium quality and eight (25%) were of high quality.

CONCLUSIONS

While decision-makers could draw vital insights from the evidence generated from mathematical modelling to inform policy, we found that there was limited use of such models exploring vaccination impacts for COVID-19 in Africa. The disparity can be addressed by scaling up mathematical modelling training, increasing collaborative opportunities between modellers and policymakers, and increasing access to funding.

Epidemiological impacts of post-infection mortality

Infectious diseases may cause some long-term damage to their host, leading to elevated mortality even after recovery. Mortality due to complications from so-called 'long COVID' is a stark illustration of this potential, but the impacts of such post-infection mortality (PIM) on epidemic dynamics are not known. Using an epidemiological model that incorporates PIM, we examine the importance of this effect. We find that in contrast to mortality during infection, PIM can induce epidemic cycling. The effect is due to interference between elevated mortality and reinfection through the previously infected susceptible pool. In particular, robust immunity (via decreased susceptibility to reinfection) reduces the likelihood of cycling; on the other hand, disease-induced mortality can interact with weak PIM to generate periodicity. In the absence of PIM, we prove that the unique endemic equilibrium is stable and therefore our key result is that PIM is an overlooked phenomenon that is likely to be destabilizing. Overall, given potentially widespread effects, our findings highlight the importance of characterizing heterogeneity in susceptibility (via both PIM and robustness of host immunity) for accurate epidemiological predictions. In particular, for diseases without robust immunity, such as SARS-CoV-2, PIM may underlie complex epidemiological dynamics especially in the context of seasonal forcing.

[Mathematical model for assessing the level of cross-immunity between strains of influenza virus subtype H3N2]

INTRODUCTION

The WHO regularly updates influenza vaccine recommendations to maximize their match with circulating strains. Nevertheless, the effectiveness of the influenza A vaccine, specifically its H3N2 component, has been low for several seasons. The aim of the study is to develop a mathematical model of cross-immunity based on the array of published WHO hemagglutination inhibition assay (HAI) data.

MATERIALS AND METHODS

In this study, a mathematical model was proposed, based on finding, using regression analysis, the dependence of HAI titers on substitutions in antigenic sites of sequences. The computer program we developed can process data (GISAID, NCBI, etc.) and create real-time databases according to the set tasks.

RESULTS

Based on our research, an additional antigenic site F was identified. The difference in 1.6 times the adjusted R2, on subsets of viruses grown in cell culture and grown in chicken embryos, demonstrates the validity of our decision to divide the original data array by passage histories. We have introduced the concept of a degree of homology between two arbitrary strains, which takes the value of a function depending on the Hamming distance, and it has been shown that the regression results significantly depend on the choice of function. The provided analysis showed that the most significant antigenic sites are A, B, and E. The obtained results on predicted HAI titers showed a good enough result, comparable to similar work by our colleagues.

CONCLUSION

The proposed method could serve as a useful tool for future forecasts, with further study to confirm its sustainability.

Expanding growers' choice of plant disease management options can promote suboptimal social outcomes

Previous models of growers' decision-making during epidemics have unrealistically limited disease management choices to just two options. Here, we expand previous game-theoretic models of grower decision-making to include three control options: a crop that is tolerant, resistant or susceptible to disease. Using tomato yellow leaf curl virus (TYLCV) as a case study, we investigate how growers can be incentivized to use different control options to achieve socially optimal outcomes. To do this, we consider the efforts of a 'social planner' who moderates the price of crops. We find that subsidizing a tolerant crop costs the social planner more in subsidies, as its use encourages selfishness and widespread adoption. Subsidizing a resistant crop, however, provides widespread benefits by reducing the prevalence of disease across the community of growers, including those that do not control, reducing the number of subsidies required from the social planner. We then use Gini coefficients to measure equitability of each subsidization scheme. This study highlights how grower behaviour can be altered using crop subsidies to promote socially optimal outcomes during epidemics.

A stratified compartmental model for the transmission of Sparicotyle chrysophrii (Platyhelminthes: Monogenea) in gilthead seabream (Sparus aurata) fish farms†

The rapid development of intensive fish farming has been associated with the spreading of infectious diseases, pathogens and parasites. One such parasite is Sparicotyle chrysophrii (Platyhelminthes: Monogenea), which commonly infects cultured gilthead seabream (Sparus aurata)-a vital species in Mediterranean aquaculture. The parasite attaches to fish gills and can cause epizootics in sea cages with relevant consequences for fish health and associated economic losses for fish farmers. In this study, a novel stratified compartmental epidemiological model of S. chrysophrii transmission was developed and analysed. The model accounts for the temporal progression of the number of juvenile and adult parasites attached to each fish, as well as the abundance of eggs and oncomiracidia. We applied the model to data collected in a seabream farm, where the fish population and the number of adult parasites attached to fish gills were closely monitored in six different cages for 10 months. The model successfully replicated the temporal dynamics of the distribution of the parasite abundance within fish hosts and simulated the effects of environmental factors, such as water temperature, on the transmission dynamics. The findings highlight the potential of modelling tools for farming management, aiding in the prevention and control of S. chrysophrii infections in Mediterranean aquaculture.

On the contact tracing for COVID-19: A simulation study☆

Background:

Contact tracing is one of the most effective non-pharmaceutical interventions in the COVID-19 pandemic. This study uses a multi-agent model to investigate the impact of four types of contact tracing strategies to prevent the spread of COVID-19.

Methods:

In order to analyse individual contact tracing in a reasonably realistic setup, we construct an agent-based model of a small municipality with about 60.000 inhabitants (nodes) and about 2.8 million social contacts (edges) in 30 different layers. Those layers reflect demographic, geographic, sociological and other patterns of the TTWA (Travel-to-work-area) Hodonín in Czechia. Various data sources such as census, land register, transport data or data reflecting the shopping behaviour, were employed to meet this purpose. On this multi-graph structure we run a modified SEIR model of the COVID-19 dynamics. The parameters of the model are calibrated on data from the outbreak in the Czech Republic in the period March to June 2020. The simplest type of contact tracing follows just the family, the second tracing version tracks the family and all the work contacts, the third type finds all contacts with the family, work contacts and friends (leisure activities). The last one is a complete (digital) tracing capable of recalling any and all contacts.

We evaluate the performance of these contact tracing strategies in four different environments. First, we consider an environment without any contact restrictions (benchmark); second with strict contact restriction (replicating the stringent non-pharmaceutical interventions employed in Czechia in the spring 2020); third environment, where the measures were substantially relaxed, and, finally an environment with weak contact restrictions and superspreader events (replicating the situation in Czechia in the summer 2020).

Findings:

There are four main findings in our paper. 1. In general, local closures are more effective than any type of tracing. 2. In an environment with strict contact restrictions there are only small differences among the four contact tracing strategies. 3. In an environment with relaxed contact restrictions the effectiveness of the tracing strategies differs substantially. 4. In the presence of superspreader events only complete contact tracing can stop the epidemic.

Interpretation:

In situations, where many other non-pharmaceutical interventions are in place, the specific extent of contact tracing may not have a large influence on their effectiveness. In a more relaxed setting with few contact restrictions and larger events the effectiveness of contact tracing depends heavily on their extent.

Inferring the disruption of rabies circulation in vampire bat populations using a betaherpesvirus-vectored transmissible vaccine

Transmissible vaccines are an emerging biotechnology that hold prospects to eliminate pathogens from wildlife populations. Such vaccines would genetically modify naturally occurring, nonpathogenic viruses ("viral vectors") to express pathogen antigens while retaining their capacity to transmit. The epidemiology of candidate viral vectors within the target wildlife population has been notoriously challenging to resolve but underpins the selection of effective vectors prior to major investments in vaccine development. Here, we used spatiotemporally replicated deep sequencing to parameterize competing epidemiological mechanistic models of Desmodus rotundus betaherpesvirus (DrBHV), a proposed vector for a transmissible vaccine targeting vampire bat-transmitted rabies. Using 36 strain- and location-specific time series of prevalence collected over 6 y, we found that lifelong infections with cycles of latency and reactivation, combined with a high R0 (6.9; CI: 4.39 to 7.85), are necessary to explain patterns of DrBHV infection observed in wild bats. These epidemiological properties suggest that DrBHV may be suited to vector a lifelong, self-boosting, and transmissible vaccine. Simulations showed that inoculating a single bat with a DrBHV-vectored rabies vaccine could immunize >80% of a bat population, reducing the size, frequency, and duration of rabies outbreaks by 50 to 95%. Gradual loss of infectious vaccine from vaccinated individuals is expected but can be countered by inoculating larger but practically achievable proportions of bat populations. Parameterizing epidemiological models using accessible genomic data brings transmissible vaccines one step closer to implementation.

Cost effectiveness of fractional doses of COVID-19 vaccine boosters in India

BACKGROUND

Coronavirus disease 2019 (COVID-19) continues to be a major global public health crisis that exacts significant human and economic costs. Booster vaccination of individuals can improve waning immunity and reduce the impact of community epidemics.

METHODS

Using an epidemiological model that incorporates population-level severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission and waning of vaccine-derived immunity, we identify the hypothetical potential of mass vaccination with fractionated vaccine doses specific to ChAdOx1 nCoV-19 (AZD1222 [Covishield]; AstraZeneca) as an optimal and cost-effective strategy in India's Omicron outbreak.

FINDINGS

We find that the optimal strategy is 1/8 fractional dosing under mild (Re ∼ 1.2) and rapid (Re ∼ 5) transmission scenarios, leading to an estimated $6 (95% confidence interval [CI]: -13, 26) billion and $2 (95% CI: -26, 30) billion in health-related net monetary benefit over 200 days, respectively. Rapid and broad use of fractional dosing for boosters, together with delivery costs divided by fractionation, could substantially gain more net monetary benefit by $11 (95% CI: -10, 33) and $2 (95% CI: -23, 28) billion, respectively, under the mild and rapid transmission scenarios.

CONCLUSIONS

Mass vaccination with fractional doses of COVID-19 vaccines to boost immunity in a vaccinated population could be a cost-effective strategy for mitigating the public health costs of resurgences caused by vaccine-evasive variants, and fractional dosing deserves further clinical and regulatory evaluation.

FUNDING

Financial support was provided by the AIR@InnoHK Program from Innovation and Technology Commission of the Government of the Hong Kong Special Administrative Region.

Disentangling the causes of mumps reemergence in the United States

Over the past two decades, multiple countries with high vaccine coverage have experienced resurgent outbreaks of mumps. Worryingly, in these countries, a high proportion of cases have been among those who have completed the recommended vaccination schedule, raising alarm about the effectiveness of existing vaccines. Two putative mechanisms of vaccine failure have been proposed as driving observed trends: 1) gradual waning of vaccine-derived immunity (necessitating additional booster doses) and 2) the introduction of novel viral genotypes capable of evading vaccinal immunity. Focusing on the United States, we conduct statistical likelihood-based hypothesis testing using a mechanistic transmission model on age-structured epidemiological, demographic, and vaccine uptake time series data. We find that the data are most consistent with the waning hypothesis and estimate that 32.8% (32%, 33.5%) of individuals lose vaccine-derived immunity by age 18 y. Furthermore, we show using our transmission model how waning vaccine immunity reproduces qualitative and quantitatively consistent features of epidemiological data, namely 1) the shift in mumps incidence toward older individuals, 2) the recent recurrence of mumps outbreaks, and 3) the high proportion of mumps cases among previously vaccinated individuals.

[Epidemiology and features of statistical accounting of in-hospital ischemic stroke (St. Petersburg experience)]

OBJECTIVE

To evaluate the effectiveness of the existing registration system and propose an epidemiological model for statistical accounting of the frequency of development of in-hospital ischemic stroke (IHS) in medical organizations of the Russian Federation on the example of St. Petersburg.

MATERIAL AND METHODS

The design of the study, conducted in the period 2014-2021, included two stages. At the first (retrospective) stage (from 01.09.14 to 31.03.16) an initiative analysis of the quality of care for 243 patients (5 medical institutions) was carried out in order to determine the relevance of the issues of IHS for the healthcare of St. Petersburg. At the second (prospective) stage, based on the data of the city stroke registry and sample control of reported cases of IHS during initiative visits and as part of annual audits, an epidemiological analysis of the frequency of occurrence of IHS in city hospitals (11 medical institutions) was performed. At the second stage, 1253 reported cases of IHS were studied: 805 (64.2%) in hospitals providing endovascular care for stroke and 448 (35.8%) in primary stroke centers (PSC). The second stage included 2 chronologically consecutive periods (from 04.01.16 to 31.12.18 and from 01.01.19 to 31.12.21) with testing of 3 different methodological approaches to accounting for the IHS.

RESULTS

The share of IHS in the structure of all ischemic strokes (IS) in hospitals with PSC and regional vascular centers (RVC) in St. Petersburg in the period 2016-2021 was 1.4-2.0%. There were no significant differences in the ratio of IHS in the overall structure of IS between typical hospitals with PSC and RVC. In the general structure of IS, initially diagnosed in hospitals, the proportion of IHS is about 1/3 (~30%), the remaining 2/3 (~70%) of cases are cases of late diagnosis of out-of-hospital vascular events (in various periods), other causes of acute cerebral pathology, cases of illegally established in-hospital vascular events.

CONCLUSION

The proposed calculation model is able to bring closer to understanding the real number of IHS in a large metropolis, but does not reflect its exact number, because is based on accounting for the work of only a part of the city hospitals included in the city's program of care for patients with stroke.

Disentangling the Factors Affecting the Dynamic of Pseudocercospora fijiensis: Quantification of Weather, Fungicide, and Landscape Effects

Quantifying the effect of landscape composition on disease dynamics remains challenging because it depends on many factors. In this study, we used a hybrid process-based/statistical modeling approach to separate the effect of the landscape composition on the epidemiology of banana leaf streak disease (BLSD) from weather and fungicide effects. We parameterized our model with a 5-year dataset, including weekly measures of BLSD on 83 plots in Martinique. After estimating the intrinsic growth parameters of the stage evolution of the disease (SED), we evaluated the dynamic effect of five fungicides. Then, we added the intra- and inter-annual effect on disease dynamics using a generalized linear model. Finally, the whole model was used to assess the annual effect of the landscape on the SED for 11 plots. We evaluated the significance of the landscape composition (proportions of landscape elements in 200-, 500-, 800-, 1,000-m-radius buffer zones) on the landscape effect evaluated with the model. The percentage of hedgerows in a 200-m-radius buffer zone was negatively correlated to the landscape effect, i.e., it acted as a constraint against BLSD spreading and development. The proportion of managed-banana-plants in a 1,000-m-radius buffer zone was negatively correlated to the landscape effect, probably due to a mass effect of fungicide treatments. Inversely, the proportions of forest and the proportion of unmanaged-banana-plants, both in 1,000-m-radius buffer zones, were positively correlated with the landscape effect. Our study provides a holistic approach of the role biotic and abiotic factors play on the dynamics of BLSD.

Improved prediction of new COVID-19 cases using a simple vector autoregressive model: evidence from seven New York state counties

With the rapid spread of COVID-19, there is an urgent need for a framework to accurately predict COVID-19 transmission. Recent epidemiological studies have found that a prominent feature of COVID-19 is its ability to be transmitted before symptoms occur, which is generally not the case for seasonal influenza and severe acute respiratory syndrome. Several COVID-19 predictive epidemiological models have been proposed; however, they share a common drawback - they are unable to capture the unique asymptomatic nature of COVID-19 transmission. Here, we propose vector autoregression (VAR) as an epidemiological county-level prediction model that captures this unique aspect of COVID-19 transmission by introducing newly infected cases in other counties as lagged explanatory variables. Using the number of new COVID-19 cases in seven New York State counties, we predicted new COVID-19 cases in the counties over the next 4 weeks. We then compared our prediction results with those of 11 other state-of-the-art prediction models proposed by leading research institutes and academic groups. The results showed that VAR prediction is superior to other epidemiological prediction models in terms of the root mean square error of prediction. Thus, we strongly recommend the simple VAR model as a framework to accurately predict COVID-19 transmission.

How the epidemiology of disease-resistant and disease-tolerant varieties affects grower behaviour

Population-scale effects of resistant or tolerant crop varieties have received little consideration from epidemiologists. When growers deploy tolerant crop, population-scale disease pressures are often unaffected. This only benefits growers using tolerant varieties, selfishly decreasing yields for others. However, resistant crop can reduce disease pressure for all. We coupled an epidemiological model with game theory to understand how this affects uptake of control. Each time a grower plants a new crop, they must decide whether to use an improved (i.e. tolerant/resistant) or unimproved variety. This decision is based on strategic-adaptive expectations in our model, with growers comparing last season's profit with an estimate of what is expected from the alternative crop. Despite the positive feedback loop promoting use of a tolerant variety whenever it is available, a mixed unimproved- and tolerant-crop equilibrium can persist. Tolerant crop can also induce bistability between a scenario in which all growers use tolerant crop and the disease-free equilibrium, where no growers do. However, due to 'free-riding' by growers of unimproved crop, resistant crop nearly always exists in a mixed equilibrium. This work highlights how growers respond to contrasting incentives caused by tolerant and resistant varieties, and the distinct effects on yields and population-scale deployment.

Capturing complex interactions in disease ecology with simplicial sets

Network approaches have revolutionized the study of ecological interactions. Social, movement and ecological networks have all been integral to studying infectious disease ecology. However, conventional (dyadic) network approaches are limited in their ability to capture higher-order interactions. We present simplicial sets as a tool that addresses this limitation. First, we explain what simplicial sets are. Second, we explain why their use would be beneficial in different subject areas. Third, we detail where these areas are: social, transmission, movement/spatial and ecological networks and when using them would help most in each context. To demonstrate their application, we develop a novel approach to identify how pathogens persist within a host population. Fourth, we provide an overview of how to use simplicial sets, highlighting specific metrics, generative models and software. Finally, we synthesize key research questions simplicial sets will help us answer and draw attention to methodological developments that will facilitate this.

Role of Foreign-Born Status on Suicide Mortality in Spain Between 2000 and 2019: An Age-Period-Cohort Analysis

Objectives: To examine recent age-period-cohort effects on suicide among foreign-born individuals, a particularly vulnerable sociodemographic group in Spain. Methods: Using 2000-2019 mortality data from Spain's National Institute of Statistics, we estimated age-period-cohort effects on suicide mortality, stratified by foreign-born status (native- vs. foreign-born) and, among the foreign-born, by Spanish citizenship status, a proxy for greater socioeconomic stability. Results: Annual suicide mortality rates were lower among foreign- than native-born individuals. There was heterogeneity in age-period-cohort effects between study groups. After 2010, suicide mortality increased markedly among the foreign-born-especially for female cohorts born around 1950, and slightly among native-born women-especially among female cohorts born after the 1960s. Among native-born men, suicide increased linearly with age and remained stable over time. Increases in suicide among the foreign-born were driven by increases among individuals without Spanish citizenship-especially among cohorts born after 1975. Conclusion: After 2010, suicide in Spain increased markedly among foreign-born individuals and slightly among native-born women, suggesting an association between the downstream effects of the 2008 economic recession and increases in suicide mortality among socioeconomically vulnerable populations.

A Transnational and Transregional Study of the Impact and Effectiveness of Social Distancing for COVID-19 Mitigation

We present an analysis of the relationship between SARS-CoV-2 infection rates and a social distancing metric from data for all the states and most populous cities in the United States and Brazil, all the 22 European Economic Community countries and the United Kingdom. We discuss why the infection rate, instead of the effective reproduction number or growth rate of cases, is a proper choice to perform this analysis when considering a wide span of time. We obtain a strong Spearman's rank order correlation between the social distancing metric and the infection rate in each locality. We show that mask mandates increase the values of Spearman's correlation in the United States, where a mandate was adopted. We also obtain an explicit numerical relation between the infection rate and the social distancing metric defined in the present work.

Infection spread simulation technology in a mixed state of multi variant viruses

ATLM (Apparent Time Lag Model) was extended to simulate the spread of infection in a mixed state of the variant virus and original wild type. It is applied to the 4th wave of infection spread in Tokyo, and (1) the 4th wave bottoms out near the end of the state of emergency, and the number of infected people increases again. (2) The rate of increase will be mainly by d strain (L452R) virus, while the increase by a strain (N501Y) virus will be suppressed. (3) It is anticipated that the infection will spread during the Olympic Games. (4) When variant viruses compete, the infection of highly infectious virus rises sharply while the infection by weakly infectious ones has converged. (5) It is effective as an infection control measure to find an infected person early and shorten the period from infection to quarantine by PCR test or antigen test as a measure other than the vaccine.

Epidemiological Predictive Modeling of COVID-19 Infection: Development, Testing, and Implementation on the Population of the Benelux Union

Since the outbreak of coronavirus disease-2019 (COVID-19), the whole world has taken interest in the mechanisms of its spread and development. Mathematical models have been valuable instruments for the study of the spread and control of infectious diseases. For that purpose, we propose a two-way approach in modeling COVID-19 spread: a susceptible, exposed, infected, recovered, deceased (SEIRD) model based on differential equations and a long short-term memory (LSTM) deep learning model. The SEIRD model is a compartmental epidemiological model with included components: susceptible, exposed, infected, recovered, deceased. In the case of the SEIRD model, official statistical data available online for countries of Belgium, Netherlands, and Luxembourg (Benelux) in the period of March 15 2020 to March 15 2021 were used. Based on them, we have calculated key parameters and forward them to the epidemiological model, which will predict the number of infected, deceased, and recovered people. Results show that the SEIRD model is able to accurately predict several peaks for all the three countries of interest, with very small root mean square error (RMSE), except for the mild cases (maximum RMSE was 240.79 ± 90.556), which can be explained by the fact that no official data were available for mild cases, but this number was derived from other statistics. On the other hand, LSTM represents a special kind of recurrent neural network structure that can comparatively learn long-term temporal dependencies. Results show that LSTM is capable of predicting several peaks based on the position of previous peaks with low values of RMSE. Higher values of RMSE are observed in the number of infected cases in Belgium (RMSE was 535.93) and Netherlands (RMSE was 434.28), and are expected because of thousands of people getting infected per day in those countries. In future studies, we will extend the models to include mobility information, variants of concern, as well as a medical intervention, etc. A prognostic model could help us predict epidemic peaks. In that way, we could react in a timely manner by introducing new or tightening existing measures before the health system is overloaded.

Dynamical analysis of novel COVID-19 epidemic model with non-monotonic incidence function

In this study, we developed and analyzed a mathematical model for explaining the transmission dynamics of COVID-19 in India. The proposed SI u I k R model is a modified version of the existing SIR model. Our model divides the infected class I of SIR model into two classes: I u (unknown infected class) and I k (known infected class). In addition, we consider R a recovered and reserved class, where susceptible people can hide them due to fear of the COVID-19 infection. Furthermore, a non-monotonic incidence function is deemed to incorporate the psychological effect of the novel coronavirus diseases on India's community. The epidemiological threshold parameter, namely the basic reproduction number, has been formulated and presented graphically. With this threshold parameter, the local and global stability analysis of the disease-free equilibrium and the endemic proportion equilibrium based on disease persistence have been analyzed. Lastly, numerical results of long-run prediction using MATLAB show that the fate of this situation is very harmful if people are not following the guidelines issued by the authority.

Chikungunya Beyond the Tropics: Where and When Do We Expect Disease Transmission in Europe?

Chikungunya virus disease (chikungunya) is a mosquito-borne infectious disease reported in at least 50 countries, mostly in the tropics. It has spread around the globe within the last two decades, with local outbreaks in Europe. The vector mosquito Aedes albopictus (Diptera, Culicidae) has already widely established itself in southern Europe and is spreading towards central parts of the continent. Public health authorities and policymakers need to be informed about where and when a chikungunya transmission is likely to take place. Here, we adapted a previously published global ecological niche model (ENM) by including only non-tropical chikungunya occurrence records and selecting bioclimatic variables that can reflect the temperate and sub-tropical conditions in Europe with greater accuracy. Additionally, we applied an epidemiological model to capture the temporal outbreak risk of chikungunya in six selected European cities. Overall, the non-tropical ENM captures all the previous outbreaks in Europe, whereas the global ENM had underestimated the risk. Highly suitable areas are more widespread than previously assumed. They are found in coastal areas of the Mediterranean Sea, in the western part of the Iberian Peninsula, and in Atlantic coastal areas of France. Under a worst-case scenario, even large areas of western Germany and the Benelux states are considered potential areas of transmission. For the six selected European cities, June–September (the 22th–38th week) is the most vulnerable time period, with the maximum continuous duration of a possible transmission period lasting up to 93 days (Ravenna, Italy).

Quantifying asymptomatic infection and transmission of COVID-19 in New York City using observed cases, serology, and testing capacity

The contributions of asymptomatic infections to herd immunity and community transmission are key to the resurgence and control of COVID-19, but are difficult to estimate using current models that ignore changes in testing capacity. Using a model that incorporates daily testing information fit to the case and serology data from New York City, we show that the proportion of symptomatic cases is low, ranging from 13 to 18%, and that the reproductive number may be larger than often assumed. Asymptomatic infections contribute substantially to herd immunity, and to community transmission together with presymptomatic ones. If asymptomatic infections transmit at similar rates as symptomatic ones, the overall reproductive number across all classes is larger than often assumed, with estimates ranging from 3.2 to 4.4. If they transmit poorly, then symptomatic cases have a larger reproductive number ranging from 3.9 to 8.1. Even in this regime, presymptomatic and asymptomatic cases together comprise at least 50% of the force of infection at the outbreak peak. We find no regimes in which all infection subpopulations have reproductive numbers lower than three. These findings elucidate the uncertainty that current case and serology data cannot resolve, despite consideration of different model structures. They also emphasize how temporal data on testing can reduce and better define this uncertainty, as we move forward through longer surveillance and second epidemic waves. Complementary information is required to determine the transmissibility of asymptomatic cases, which we discuss. Regardless, current assumptions about the basic reproductive number of severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) should be reconsidered.

Modeling Mongoose Rabies in the Caribbean: A Model-Guided Fieldwork Approach to Identify Research Priorities

We applied the model-guided fieldwork framework to the Caribbean mongoose rabies system by parametrizing a spatially-explicit, individual-based model, and by performing an uncertainty analysis designed to identify parameters for which additional empirical data are most needed. Our analysis revealed important variation in output variables characterizing rabies dynamics, namely rabies persistence, exposure level, spatiotemporal distribution, and prevalence. Among epidemiological parameters, rabies transmission rate was the most influential, followed by rabies mortality and location, and size of the initial infection. The most influential landscape parameters included habitat-specific carrying capacities, landscape heterogeneity, and the level of resistance to dispersal associated with topography. Movement variables, including juvenile dispersal, adult fine-scale movement distances, and home range size, as well as life history traits such as age of independence, birth seasonality, and age- and sex-specific mortality were other important drivers of rabies dynamics. We discuss results in the context of mongoose ecology and its influence on disease transmission dynamics. Finally, we suggest empirical approaches and study design specificities that would provide optimal contributing data addressing the knowledge gaps identified by our approach, and would increase our potential to use epidemiological models to guide mongoose rabies control and management in the Caribbean.

On the Transmission Dynamics of SARS-CoV-2 in a Temperate Climate

An epidemiological model, which describes the transmission dynamics of SARS-CoV-2 under specific consideration of the incubation period including the population with subclinical infections and being infective is presented. The COVID-19 epidemic in Greece was explored through a Monte Carlo uncertainty analysis framework, and the optimal values for the parameters that determined the transmission dynamics could be obtained before, during, and after the interventions to control the epidemic. The dynamic change of the fraction of asymptomatic individuals was shown. The analysis of the modelling results at the intra-annual climatic scale allowed for in depth investigation of the transmission dynamics of SARS-CoV-2 and the significance and relative importance of the model parameters. Moreover, the analysis at this scale incorporated the exploration of the forecast horizon and its variability. Three discrete peaks were found in the transmission rates throughout the investigated period (15 February–15 December 2020). Two of them corresponded to the timing of the spring and autumn epidemic waves while the third one occurred in mid-summer, implying that relaxation of social distancing and increased mobility may have a strong effect on rekindling the epidemic dynamics offsetting positive effects from factors such as decreased household crowding and increased environmental ultraviolet radiation. In addition, the epidemiological state was found to constitute a significant indicator of the forecast reliability horizon, spanning from as low as few days to more than four weeks. Embedding the model in an ensemble framework may extend the predictability horizon. Therefore, it may contribute to the accuracy of health risk assessment and inform public health decision making of more efficient control measures.

An Epidemiological Model Considering Isolation to Predict COVID-19 Trends in Tokyo, Japan: Numerical Analysis

BACKGROUND

COVID-19 currently poses a global public health threat. Although Tokyo, Japan, is no exception to this, it was initially affected by only a small-level epidemic. Nevertheless, medical collapse nearly happened since no predictive methods were available to assess infection counts. A standard susceptible-infectious-removed (SIR) epidemiological model has been widely used, but its applicability is limited often to the early phase of an epidemic in the case of a large collective population. A full numerical simulation of the entire period from beginning until end would be helpful for understanding COVID-19 trends in (separate) counts of inpatient and infectious cases and can also aid the preparation of hospital beds and development of quarantine strategies.

OBJECTIVE

This study aimed to develop an epidemiological model that considers the isolation period to simulate a comprehensive trend of the initial epidemic in Tokyo that yields separate counts of inpatient and infectious cases. It was also intended to induce important corollaries of governing equations (ie, effective reproductive number) and equations for the final count.

METHODS

Time-series data related to SARS-CoV-2 from February 28 to May 23, 2020, from Tokyo and antibody testing conducted by the Japanese government were adopted for this study. A novel epidemiological model based on a discrete delay differential equation (apparent time-lag model [ATLM]) was introduced. The model can predict trends in inpatient and infectious cases in the field. Various data such as daily new confirmed cases, cumulative infections, inpatients, and PCR (polymerase chain reaction) test positivity ratios were used to verify the model. This approach also derived an alternative formulation equivalent to the standard SIR model.

RESULTS

In a typical parameter setting, the present ATLM provided 20% less infectious cases in the field compared to the standard SIR model prediction owing to isolation. The basic reproductive number was inferred as 2.30 under the condition that the time lag T from infection to detection and isolation is 14 days. Based on this, an adequate vaccine ratio to avoid an outbreak was evaluated for 57% of the population. We assessed the date (May 23) that the government declared a rescission of the state of emergency. Taking into consideration the number of infectious cases in the field, a date of 1 week later (May 30) would have been most effective. Furthermore, simulation results with a shorter time lag of T=7 and a larger transmission rate of α=1.43α0 suggest that infections at large should reduce by half and inpatient numbers should be similar to those of the first wave of COVID-19.

CONCLUSIONS

A novel mathematical model was proposed and examined using SARS-CoV-2 data for Tokyo. The simulation agreed with data from the beginning of the pandemic. Shortening the period from infection to hospitalization is effective against outbreaks without rigorous public health interventions and control.

Control of Brucella melitensis in endemic settings: A simulation study in the Nile Delta, Egypt

Small ruminant brucellosis remains endemic in many low- and middle-income countries (LMICs), where it poses a major economic and public health burden. Lack of resources to support long-term vaccination, inherent characteristics of small ruminant production systems such as mixing of different flocks for grazing and limitations of the vaccines currently available, which can induce abortion in pregnant animals, have all hindered the effectiveness of control programmes. In the current study, the likely effect of different control scenarios on the seroprevalence of brucellosis among the small ruminant population in a hypothetical area of an endemic region was simulated using compartmental models. The model accounts for variability in transmission rates between villages and also simulates control scenarios that target villages with high seroprevalence. Our results show that vaccination of young replacement animals only can effectively reduce the prevalence of small ruminant brucellosis in endemic settings if a high vaccination coverage is achieved. On the other hand, test-and-slaughter alone is not a promising strategy for control of small ruminant brucellosis under husbandry practices typical of endemic low-resource settings. Furthermore, results show the potential success of some strategies requiring a relatively low overall vaccination coverage such as the vaccination of 50% of young replacements and 25% of adult animals each year. Control strategies selectively targeting high initial seroprevalence villages (p > 10%) did not decrease the overall seroprevalence to acceptable levels in most of the examined scenarios. Scenario analysis showed that the efficacy of the simulated control strategies can be improved mostly by decreasing the proportion of between-village trade and also by improving the performance of the used serological tests and increasing vaccine efficacy.

Estimating epidemic coupling between populations from the time to invasion

Identifying the mechanisms by which diseases spread among populations is important for understanding and forecasting patterns of epidemics and pandemics. Estimating transmission coupling among populations is challenging because transmission events are difficult to observe in practice, and connectivity among populations is often obscured by local disease dynamics. We consider the common situation in which an epidemic is seeded in one population and later spreads to a second population. We present a method for estimating transmission coupling between the two populations, assuming they can be modelled as susceptible-infected-removed (SIR) systems. We show that the strength of coupling between the two populations can be estimated from the time taken for the disease to invade the second population. Confidence in the estimate is low if only a single invasion event has been observed, but is substantially improved if numerous independent invasion events are observed. Our analysis of this simplest, idealized scenario represents a first step toward developing and verifying methods for estimating epidemic coupling among populations in an ever-more-connected global human population.

Eco-Epidemiological Uncertainties of Emerging Plant Diseases: The Challenge of Predicting Xylella fastidiosa Dynamics in Novel Environments

In order to prevent and control the emergence of biosecurity threats such as vector-borne diseases of plants, it is vital to understand drivers of entry, establishment, and spatiotemporal spread, as well as the form, timing, and effectiveness of disease management strategies. An inherent challenge for policy in combatting emerging disease is the uncertainty associated with intervention planning in areas not yet affected, based on models and data from current outbreaks. Following the recent high-profile emergence of the bacterium Xylella fastidiosa in a number of European countries, we review the most pertinent epidemiological uncertainties concerning the dynamics of this bacterium in novel environments. To reduce the considerable ecological and socio-economic impacts of these outbreaks, eco-epidemiological research in a broader range of environmental conditions needs to be conducted and used to inform policy to enhance disease risk assessment, and support successful policy-making decisions. By characterizing infection pathways, we can highlight the uncertainties that surround our knowledge of this disease, drawing attention to how these are amplified when trying to predict and manage outbreaks in currently unaffected locations. To help guide future research and decision-making processes, we invited experts in different fields of plant pathology to identify data to prioritize when developing pest risk assessments. Our analysis revealed that epidemiological uncertainty is mainly driven by the large variety of hosts, vectors, and bacterial strains, leading to a range of different epidemiological characteristics further magnified by novel environmental conditions. These results offer new insights on how eco-epidemiological analyses can enhance understanding of plant disease spread and support management recommendations.[Formula: see text] Copyright © 2020 The Author(s). This is an open access article distributed under the CC BY 4.0 International license.

Transient indicators of tipping points in infectious diseases

The majority of known early warning indicators of critical transitions rely on asymptotic resilience and critical slowing down. In continuous systems, critical slowing down is mathematically described by a decrease in magnitude of the dominant eigenvalue of the Jacobian matrix on the approach to a critical transition. Here, we show that measures of transient dynamics, specifically, reactivity and the maximum of the amplification envelope, also change systematically as a bifurcation is approached in an important class of models for epidemics of infectious diseases. Furthermore, we introduce indicators designed to detect trends in these measures and find that they reliably classify time series of case notifications simulated from stochastic models according to levels of vaccine uptake. Greater attention should be focused on the potential for systems to exhibit transient amplification of perturbations as a critical threshold is approached, and should be considered when searching for generic leading indicators of tipping points. Awareness of this phenomenon will enrich understanding of the dynamics of complex systems on the verge of a critical transition.

A COVID-19-Based Modified Epidemiological Model and Technological Approaches to Help Vulnerable Individuals Emerge from the Lockdown in the UK

COVID-19 has shown a relatively low case fatality rate in young healthy individuals, with the majority of this group being asymptomatic or having mild symptoms. However, the severity of the disease among the elderly as well as in individuals with underlying health conditions has caused significant mortality rates worldwide. Understanding this variance amongst different sectors of society and modelling this will enable the different levels of risk to be determined to enable strategies to be applied to different groups. Long-established compartmental epidemiological models like SIR and SEIR do not account for the variability encountered in the severity of the SARS-CoV-2 disease across different population groups. The objective of this study is to investigate how a reduction in the exposure of vulnerable individuals to COVID-19 can minimise the number of deaths caused by the disease, using the UK as a case study. To overcome the limitation of long-established compartmental epidemiological models, it is proposed that a modified model, namely SEIR-v, through which the population is separated into two groups regarding their vulnerability to SARS-CoV-2 is applied. This enables the analysis of the spread of the epidemic when different contention measures are applied to different groups in society regarding their vulnerability to the disease. A Monte Carlo simulation (100,000 runs) along the proposed SEIR-v model is used to study the number of deaths which could be avoided as a function of the decrease in the exposure of vulnerable individuals to the disease. The results indicate a large number of deaths could be avoided by a slight realistic decrease in the exposure of vulnerable groups to the disease. The mean values across the simulations indicate 3681 and 7460 lives could be saved when such exposure is reduced by 10% and 20% respectively. From the encouraging results of the modelling a number of mechanisms are proposed to limit the exposure of vulnerable individuals to the disease. One option could be the provision of a wristband to vulnerable people and those without a smartphone and contact-tracing app, filling the gap created by systems relying on smartphone apps only. By combining very dense contact tracing data from smartphone apps and wristband signals with information about infection status and symptoms, vulnerable people can be protected and kept safer.

An estimate of the incidence and quantitative risk assessment of human brucellosis in mainland China

Two epidemiological models were applied to simulate whether animals with latent infections were contagious and calculate the outcomes of people that contracting brucellosis by all possible transmission routes under control measures implemented by the Chinese government. The health and economic burden of brucellosis overall presented an increasing trend from 2004 to 2017. Scenarios from epidemiological models showed that a larger scale of vaccine coverage would contribute to fewer infections in livestock and humans. S2 vaccine, the disinfection of the environment and the protection of the susceptible animals and humans could effectively reverse the trend of increasing brucellosis and reduce the incidence rates of brucellosis in humans to curb the epidemic of brucellosis in China.

Illustration of Different Disease Transmission Routes in a Pig Trade Network by Monopartite and Bipartite Representation

Simple Summary

Besides direct animal movements between farms; indirect transmission routes of pathogens can have an immense impact on network structure and disease spread in animal trade networks. This study integrated these indirect transmission routes between farms via transport companies or feed supply as bipartite networks; which were compared to the monopartite animal movements network representing the direct transmission route. Both bipartite networks were projected on farm level to enable a comparison to the monopartite network. The number of edges increased immensely from the monopartite animal movements network to both projected networks. Thus, farms can be highly connected over indirect connections, although they are not directly trading animals. The ranking of the animals according to their centrality parameters, indicating their importance for the network, showed moderate correlations only between the animal movements and the transportation network. The epidemiological models based on the different network representations revealed significantly more infected farms for the networks including indirect transmission routes compared to the direct animal movements. Indirect transmission routes had an immense impact on the outcome of centrality parameters, as well as on the spreading process within the network. This knowledge is needed to understand disease spread and to establish reliable prevention and control measurements.

Abstract

Besides the direct transport of animals, also indirect transmission routes, e.g., contact via contaminated vehicles, have to be considered. In this study, the transmission routes of a German pig trade network were illustrated as a monopartite animal movements network and two bipartite networks including information of the transport company and the feed producer which were projected on farm level (n = 866) to enable a comparison. The networks were investigated with the help of network analysis and formed the basis for epidemiological models to evaluate the impact of different transmission routes on network structure as well as on potential epidemic sizes. The number of edges increased immensely from the monopartite animal movements network to both projected networks. The median centrality parameters revealed clear differences between the three representations. Furthermore, moderate correlation coefficients ranging from 0.55 to 0.68 between the centrality values of the animal movements network and the projected transportation network were obtained. The epidemiological models revealed significantly more infected farms for both projected networks (70% to 100%) compared to the animal movements network (1%). The inclusion of indirect transmission routes had an immense impact on the outcome of centrality parameters as well as on the results of the epidemiological models.

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.

ESTIMATING AGE-SPECIFIC HAZARD RATES OF INFECTION FROM CROSS-SECTIONAL OBSERVATIONS

Mathematical models of pathogen transmission in age-structured host populations, can be used to design or evaluate vaccination programs. For reliable results, their forces or hazard rates of infection (FOI) must be formulated correctly and the requisite contact rates and probabilities of infection on contact estimated from suitable observations. Elsewhere, we have described methods for calculating the probabilities of infection on contact from the contact rates and FOI. Here, we present methods for estimating the FOI from cross-sectional serological surveys or disease surveillance in populations with or without concurrent vaccination. We consider both continuous and discrete age, and present estimates of the FOI for vaccine-preventable diseases that confer temporary or permanent immunity.

Impact of Genetic Selection for Increased Cattle Resistance to Bovine Tuberculosis on Disease Transmission Dynamics

Bovine tuberculosis (bTB) poses a challenge to animal health and welfare worldwide. Presence of genetic variation in host resistance to Mycobacterium bovis infection makes the trait amenable to improvement with genetic selection. Genetic evaluations for resistance to infection in dairy cattle are currently available in the United Kingdom (UK), enabling genetic selection of more resistant animals. However, the extent to which genetic selection could contribute to bTB eradication is unknown. The objective of this study was to quantify the impact of genetic selection for bTB resistance on cattle-to-cattle disease transmission dynamics and prevalence by developing a stochastic genetic epidemiological model. The model was used to implement genetic selection in a simulated cattle population. The model considered various levels of selection intensity over 20 generations assuming genetic heterogeneity in host resistance to infection. Our model attempted to represent the dairy cattle population structure and current bTB control strategies in the UK, and was informed by genetic and epidemiological parameters inferred from data collected from UK bTB infected dairy herds. The risk of a bTB breakdown was modeled as the percentage of herds where initially infected cows (index cases) generated secondary cases by infecting herd-mates. The model predicted that this risk would be reduced by half after 4, 6, 9, and 15 generations for selection intensities corresponding to genetic selection of the 10, 25, 50, and 70% most resistant sires, respectively. In herds undergoing bTB breakdowns, genetic selection reduced the severity of breakdowns over generations by reducing both the percentage of secondary cases and the duration over which new secondary cases were detected. Selection of the 10, 25, 50, and 70% most resistant sires reduced the percentage of secondary cases to <1% in 4, 5, 7, and 11 generations, respectively. Similarly, the proportion of long breakdowns (breakdowns in which secondary cases were detected for more than 365 days) was reduced by half in 2, 2, 3, and 4 generations, respectively. Collectively, results suggest that genetic selection could be a viable tool that can complement existing management and surveillance methods to control and ultimately eradicate bTB.

Pierce's Disease of Grapevines: A Review of Control Strategies and an Outline of an Epidemiological Model

Xylella fastidiosa is a notorious plant pathogenic bacterium that represents a threat to crops worldwide. Its subspecies, Xylella fastidiosa subsp. fastidiosa is the causal agent of Pierce's disease of grapevines. Pierce's disease has presented a serious challenge for the grapevine industry in the United States and turned into an epidemic in Southern California due to the invasion of the insect vector Homalodisca vitripennis. In an attempt to minimize the effects of Xylella fastidiosa subsp. fastidiosa in vineyards, various studies have been developing and testing strategies to prevent the occurrence of Pierce's disease, i.e., prophylactic strategies. Research has also been undertaken to investigate therapeutic strategies to cure vines infected by Xylella fastidiosa subsp. fastidiosa. This report explicitly reviews all the strategies published to date and specifies their current status. Furthermore, an epidemiological model of Xylella fastidiosa subsp. fastidiosa is proposed and key parameters for the spread of Pierce's disease deciphered in a sensitivity analysis of all model parameters. Based on these results, it is concluded that future studies should prioritize therapeutic strategies, while investments should only be made in prophylactic strategies that have demonstrated promising results in vineyards.

Foot-and-mouth disease virus transmission dynamics and persistence in a herd of vaccinated dairy cattle in India

Foot-and-mouth disease (FMD) is an important transboundary disease with substantial economic impacts. Although between-herd transmission of the disease has been well studied, studies focusing on within-herd transmission using farm-level outbreak data are rare. The aim of this study was to estimate parameters associated with within-herd transmission, host physiological factors and FMD virus (FMDV) persistence using data collected from an outbreak that occurred at a large, organized dairy farm in India. Of 1,836 regularly vaccinated, adult dairy cattle, 222 had clinical signs of FMD over a 39-day period. Assuming homogenous mixing, a frequency-dependent compartmental model of disease transmission was built. The transmission coefficient and basic reproductive number were estimated to be between 16.2-18.4 and 67-88, respectively. Non-pregnant animals were more likely to manifest clinical signs of FMD as compared to pregnant cattle. Based on oropharyngeal fluid (probang) sampling and FMDV-specific RT-PCR, four of 36 longitudinally sampled animals (14%) were persistently infected carriers 10.5 months post-outbreak. There was no statistical difference between subclinical and clinically infected animals in the duration of the carrier state. However, prevalence of NSP-ELISA antibodies differed significantly between subclinical and clinically infected animals 12 months after the outbreak with 83% seroprevalence amongst clinically infected cattle compared to 69% of subclinical animals. This study further elucidates within-herd FMD transmission dynamics during the acute-phase and characterizes duration of FMDV persistence and seroprevalence of FMD under natural conditions in an endemic setting.

Dynamics of host populations affected by the emerging fungal pathogen Batrachochytrium salamandrivorans

Emerging infectious diseases cause extirpation of wildlife populations. We use an epidemiological model to explore the effects of a recently emerged disease caused by the salamander-killing chytrid fungus Batrachochytrium salamandrivorans (Bsal) on host populations, and to evaluate which mitigation measures are most likely to succeed. As individuals do not recover from Bsal, we used a model with the states susceptible, latent and infectious, and parametrized the model using data on host and pathogen taken from the literature and expert opinion. The model suggested that disease outbreaks can occur at very low host densities (one female per hectare). This density is far lower than host densities in the wild. Therefore, all naturally occurring populations are at risk. Bsal can lead to the local extirpation of the host population within a few months. Disease outbreaks are likely to fade out quickly. A spatial variant of the model showed that the pathogen could potentially spread rapidly. As disease mitigation during outbreaks is unlikely to be successful, control efforts should focus on preventing disease emergence and transmission between populations. Thus, this emerging wildlife disease is best controlled through prevention rather than subsequent actions.

Intrinsic and realized generation intervals in infectious-disease transmission

The generation interval is the interval between the time when an individual is infected by an infector and the time when this infector was infected. Its distribution underpins estimates of the reproductive number and hence informs public health strategies. Empirical generation-interval distributions are often derived from contact-tracing data. But linking observed generation intervals to the underlying generation interval required for modelling purposes is surprisingly not straightforward, and misspecifications can lead to incorrect estimates of the reproductive number, with the potential to misguide interventions to stop or slow an epidemic. Here, we clarify the theoretical framework for three conceptually different generation-interval distributions: the 'intrinsic' one typically used in mathematical models and the 'forward' and 'backward' ones typically observed from contact-tracing data, looking, respectively, forward or backward in time. We explain how the relationship between these distributions changes as an epidemic progresses and discuss how empirical generation-interval data can be used to correctly inform mathematical models.

Accurate prediction of black rot epidemics in vineyards using a weather-driven disease model

BACKGROUND

Grapevine black rot caused by Guignardia bidwellii is a serious threat in vineyards, especially in areas with cool and humid springs. A mechanistic, weather-driven model was recently developed for the detailed prediction of black rot epidemics. The aim of this work was to evaluate the model by comparison with observed disease development in leaves and clusters in a vineyard in north Italy from 2013 to 2015.

RESULTS

The model accurately predicted disease onset. The probability of predicting new infections that did not occur (i.e. unjustified alarms) was ≤0.180, while the probability of missing actual infections was 0.175 for leaves and 0.263 for clusters. In 78% of these false negative predictions, the difference between expected and actual disease onset was ±2 days; therefore, only one infection period was actually missed by the model. The model slightly overestimated disease severity (mainly on leaves) when the observed disease severity was >0.6.

CONCLUSION

The model was highly accurate and robust in predicting the infection periods and dynamics of black rot epidemics. The model can be used for scheduling fungicide sprays in vineyards. © 2016 Society of Chemical Industry.

Limited Specificity in the Injury and Infection Priming against Bacteria in Aedes aegypti Mosquitoes

Injury and infection priming has been observed in several insect groups, reported as host immune protection against contact with a pathogen caused by a previous infection with the same. However, the specific response against a pathogen has not been demonstrated in all insect species. Investigating the specific priming response in insects is important because their immune strategies probably reflect particular selective pressures exerted by different pathogens. Here, we determined whether previous infection of Aedes aegypti would enhance survival and/or lead to greater and specific AMP expression after a second exposure to the same or a distinct bacterium. Mosquitoes previously immunized with a low dose of Escherichia coli, but not Staphylococcus aureus, showed increased survival. Although the host protection herein demonstrated was not specific, each bacterium elicited differential AMP expression. These results can be explained by the susceptible-primed-infected (SPI) epidemiological model, which poses that in the evolution of memory-like responses (priming), a pivotal role is played by pathogen virulence, associated host damage, and the host capacity of pathogen recognition.

Differential and enhanced response to climate forcing in diarrheal disease due to rotavirus across a megacity of the developing world

The role of climate forcing in the population dynamics of infectious diseases has typically been revealed via retrospective analyses of incidence records aggregated across space and, in particular, over whole cities. Here, we focus on the transmission dynamics of rotavirus, the main diarrheal disease in infants and young children, within the megacity of Dhaka, Bangladesh. We identify two zones, the densely urbanized core and the more rural periphery, that respond differentially to flooding. Moreover, disease seasonality differs substantially between these regions, spanning variation comparable to the variation from tropical to temperate regions. By combining process-based models with an extensive disease surveillance record, we show that the response to climate forcing is mainly seasonal in the core, where a more endemic transmission resulting from an asymptomatic reservoir facilitates the response to the monsoons. The force of infection in this monsoon peak can be an order of magnitude larger than the force of infection in the more epidemic periphery, which exhibits little or no postmonsoon outbreak in a pattern typical of nearby rural areas. A typically smaller peak during the monsoon season nevertheless shows sensitivity to interannual variability in flooding. High human density in the core is one explanation for enhanced transmission during troughs and an associated seasonal monsoon response in this diarrheal disease, which unlike cholera, has not been widely viewed as climate-sensitive. Spatial demographic, socioeconomic, and environmental heterogeneity can create reservoirs of infection and enhance the sensitivity of disease systems to climate forcing, especially in the populated cities of the developing world.

Modeling the Spread of Ebola

Objectives

This study aims to create a mathematical model to better understand the spread of Ebola, the mathematical dynamics of the disease, and preventative behaviors.

Methods

An epidemiological model is created with a system of nonlinear differential equations, and the model examines the disease transmission dynamics with isolation through stability analysis. All parameters are approximated, and results are also exploited by simulations. Sensitivity analysis is used to discuss the effect of intervention strategies.

Results

The system has only one equilibrium point, which is the disease-free state (S,L,I,R,D) = (N,0,0,0,0). If traditional burials of Ebola victims are allowed, the possible end state is never stable. Provided that safe burial practices with no traditional rituals are followed, the endemic-free state is stable if the basic reproductive number, R₀, is less than 1. Model behaviors correspond to empirical facts. The model simulation agrees with the data of the Nigeria outbreak in 2004: 12 recoveries, eight deaths, Ebola free in about 3 months, and an R₀ value of about 2.6 initially, which signifies swift spread of the infection. The best way to reduce R₀ is achieving the speedy net effect of intervention strategies. One day's delay in full compliance with building rings around the virus with isolation, close observation, and clear education may double the number of infected cases.

Conclusion

The model can predict the total number of infected cases, number of deaths, and duration of outbreaks among others. The model can be used to better understand the spread of Ebola, educate about prophylactic behaviors, and develop strategies that alter environment to achieve a disease-free state. A future work is to incorporate vaccination in the model when the vaccines are developed and the effects of vaccines are known better.

Quantifying the reliability of dispersal paths in connectivity networks

Many biological systems, from fragmented landscapes to host populations, can be represented as networks of connected habitat patches. Links between patches in these connectivity networks can represent equally diverse processes, from individuals moving through the landscape to pathogen transmissions or successive colonization events in metapopulations. Any of these processes can be characterized as stochastic, with functional links among patches that exist with various levels of certainty. This stochasticity then needs to be reflected in the algorithms that aim to predict the dispersal routes in these networks. Here we adapt the concept of reliability to characterize the likelihood that a specific path will be used for dispersal in a probabilistic connectivity network. The most reliable of the paths that connect two patches will then identify the most likely sequence of intermediate steps between these patches. Path reliability will be sensitive to targeted disruptions of individual links that form the path, and this can then be used to plan the interventions aimed at either preserving or disrupting the dispersal along that path. The proposed approach is general, and can be used to identify the most likely dispersal routes in various contexts, such as predicting patterns of migrations, colonizations, invasions and epidemics.

Dissecting the determinants of malaria chronicity: why within-host models struggle to reproduce infection dynamics

The duration of infection is fundamental to the epidemiological behaviour of any infectious disease, but remains one of the most poorly understood aspects of malaria. In endemic areas, the malaria parasite Plasmodium falciparum can cause both acute, severe infections and asymptomatic, chronic infections through its interaction with the host immune system. Frequent superinfection and massive parasite genetic diversity make it extremely difficult to accurately measure the distribution of infection lengths, complicating the estimation of basic epidemiological parameters and the prediction of the impact of interventions. Mathematical models have qualitatively reproduced parasite dynamics early during infection, but reproducing long-lived chronic infections remains much more challenging. Here, we construct a model of infection dynamics to examine the consequences of common biological assumptions for the generation of chronicity and the impact of co-infection. We find that although a combination of host and parasite heterogeneities are capable of generating chronic infections, they do so only under restricted parameter choices. Furthermore, under biologically plausible assumptions, co-infection of parasite genotypes can alter the course of infection of both the resident and co-infecting strain in complex non-intuitive ways. We outline the most important puzzles for within-host models of malaria arising from our analysis, and their implications for malaria epidemiology and control.

Optimal implementation of intervention strategies for elderly people with ludomania

Objectives

Now-a-days gambling is growing especially fast among older adults. To control the gratuitous growth of gambling, well-analyzed scientific strategies are necessary. We tried to analyze the adequacy of the health of society mathematically through immediate treatment of patients with early prevention.

Methods

The model from Lee and Do was modified and control parameters were introduced. Pontryagin's Maximum Principle was used to obtain an optimal control strategy.

Results

Optimal control can be achieved through simultaneous use of the control parameters, though it varies from society to society. The control corresponding to prevention needed to be implemented in full almost all the time for all types of societies. In the case of the other two controls, the scenario was greatly affected depending on the types of societies.

Conclusion

Prevention and treatment for elderly people with ludomania are the main intervention strategies. We found that optimal timely implementation of the intervention strategies was more effective. The optimal control strategy varied with the initial number of gamblers. However, three intervention strategies were considered, among which, preventing people from engaging in all types of gambling proved to be the most crucial.

Optimal Implementation of Intervention to Control the Self-harm Epidemic

Objectives

Deliberate self-harm (DSH) of a young person has been a matter of growing concern to parents and policymakers. Prevention and early eradication are the main interventional techniques among which prevention through reducing peer pressure has a major role in reducing the DSH epidemic. Our aim is to develop an optimal control strategy for minimizing the DSH epidemic and to assess the efficacy of the controls.

Methods

We considered a deterministic compartmental model of the DSH epidemic and two interventional techniques as the control measures. Pontryagin's Maximum Principle was used to mathematically derive the optimal controls. We also simulated the model using the forward-backward sweep method.

Results

Simulation results showed that the controls needed to be used simultaneously to reduce DSH successfully. An optimal control strategy should be adopted, depending on implementation costs for the controls.

Conclusion

The long-term success of the optimum control depends on the implementation cost. If the cost is very high, the control could be used for a short term, even though it fails in the long run. The control strategy, most importantly, should be implemented as early as possible to attack a comparatively fewer number of addicted individuals.

Assessing the potential spread and maintenance of foot-and-mouth disease virus infection in wild ungulates: general principles and application to a specific scenario in Thrace

Foot-and-mouth disease (FMD), due to infection with serotype O virus, occurred in wild boar and within eleven outbreaks in domestic livestock in the south-east of Bulgaria, Thrace region, in 2011. Hence, the issue of the potential for the spread and maintenance of FMD virus (FMDV) infection in a population of wild ungulates became important. This assessment focused on the spread and maintenance of FMDV infection within a hypothetical wild boar and deer population in an environment, which is characterized by a climate transitional between Mediterranean and continental and variable wildlife population densities. The assessment was based on three aspects: (i) a systematic review of the literature focusing on experimental infection studies to identify the parameters describing the duration of FMDV infection in deer and wild boar, as well as observational studies assessing the occurrence of FMDV infection in wild deer and wild boar populations, (ii) prevalence survey data of wild boar and deer in Bulgaria and Turkey and (iii) an epidemiological model, simulating the host-to-host spread of FMDV infections. It is concluded, based on all three aspects, that the wildlife population in Thrace, and so wildlife populations in similar ecological settings, are probably not able to maintain FMD in the long term in the absence of FMDV infection in the domestic host population. However, limited spread of FMDV infection in time and space in the wildlife populations can occur. If there is a continued cross-over of FMDV between domestic and wildlife populations or a higher population density, virus circulation may be prolonged.

Frequency-dependent assistance as a way out of competitive exclusion between two strains of an emerging virus

Biological invasions are the main causes of emerging viral diseases and they favour the co-occurrence of multiple species or strains in the same environment. Depending on the nature of the interaction, co-occurrence can lead to competitive exclusion or coexistence. The successive fortuitous introductions of two strains of Tomato yellow leaf curl virus (TYLCV-Mld and TYLCV-IL) in Réunion Island provided an ideal opportunity to study the invasion of, and competition between, these worldwide emerging pathogens. During a 7-year field survey, we observed a displacement of the resident TYLCV-Mld by the newcomer TYLCV-IL, with TYLCV-Mld remaining mostly in co-infected plants. To understand the factors associated with this partial displacement, biological traits related to fitness were measured. The better ecological aptitude of TYLCV-IL in single infections was demonstrated, which explains its rapid spread. However, we demonstrate that the relative fitness of virus strains can drastically change between single infections and co-infections. An epidemiological model parametrized with our experimental data predicts that the two strains will coexist in the long run through assistance by the fitter strain. This rare case of unilateral facilitation between two pathogens leads to frequency-dependent selection and maintenance of the less fit strain.

Optimal Control Strategy of Plasmodium vivax Malaria Transmission in Korea

Objective

To investigate the optimal control strategy for Plasmodium vivax malaria transmission in Korea.

Methods

A Plasmodium vivax malaria transmission model with optimal control terms using a deterministic system of differential equations is presented, and analyzed mathematically and numerically.

Results

If the cost of reducing the reproduction rate of the mosquito population is more than that of prevention measures to minimize mosquito-human contacts, the control of mosquito-human contacts needs to be taken for a longer time, comparing the other situations. More knowledge about the actual effectiveness and costs of control intervention measures would give more realistic control strategies.

Conclusion

Mathematical model and numerical simulations suggest that the use of mosquito-reduction strategies is more effective than personal protection in some cases but not always.

Parametric Uncertainty in Intra-Herd Foot-and-Mouth Disease Epidemiological Models

Objective

The objective of this project is to understand how parametric uncertainty within intra-herd Foot-and-Mouth disease epidemiological models affects the outbreak simulations and what implications this has on surveillance and control strategy and policy.

Introduction

The rapid transmission and poor control policy response during recent Foot-and-Mouth disease (FMD) outbreaks have underscored the need for better decision support tools. At the foundation of these decision support tools are the epidemiological models that are parameterized with the data generated from pathogenesis studies of the FMD virus that contain contact transmission data. These values being used to parameterize the model, contrary to assumption, contain a significant amount of uncertainty, which propagates throughout the model affecting output. To understand how parametric uncertainty might affect output, a variety of disease transmission parameters were generated from contact transmission data and parameterized to an intra-herd model.

Methods

Data was initially collected and analyzed for papers that could meet several criteria: they must be contact transmission studies, they must measure viremia (the level of virus in the blood), and they must observe clinical signs.

For the studies that met the criteria, tables were constructed and the following information from each paper was collected: serotype, strain, animal species, unique animal identifier, unit of measurement utilized by virus quantification, duration and quantity of viremia, and the time to first report of clinical signs.

Three different durations of disease states for the latent, sub-clinically infectious, and clinically infectious periods were generated from the viremia data for each individual animal and grouped in three ways: by strain of virus, by similar experimental design, and all together. Gamma, weibull, and normal distributions were fitted to the data in each group.

The distributions for each group were then used to parameterize a stochastic, state transition intra-herd model. Output from the model was analyzed by examining the uncertainty and variance in time to 50% herd infected, time to 2% herd clinically infected, and percentage of herd infected at 2% herd clinically infected for each distribution and group.

Results

There is a lack of a standardized definition for disease state durations of the Foot-and-Mouth Disease virus in the literature. As a result, many different models utilize slightly differing values generated from the same data. This project discovered that depending on the definitions used to determine the disease state durations, the model output varied significantly. Additionally, durations of the disease state periods do not follow a normal distribution as may be assumed by many modelers, and are more accurately described by distributions that allow for non-zero skewness.

Conclusions

The data being used to parameterize intra-herd Foot-and-Mouth disease models contains a significant amount of uncertainty that can cause the model output to vary significantly. This uncertainty needs to be clearly communicated to decision makers who use results generated from FMD intra-herd models and illustrates the need for more resources to be put into addressing the issue of basic parameters such as contact rate and disease state duration. Currently no studies have been conducted on the contact rate of animals on farms and the current values used for disease state durations vary drastically depending on the data and methods used. Without a better understanding of the basic parameters, even the most advanced models will not be accurate.