Movement-driven modelling reveals new patterns in disease transmission networks.

Interspecific interactions are highly relevant in the potential transmission of shared pathogens in multi-host systems. In recent decades, several technologies have been developed to study pathogen transmission, such as proximity loggers, GPS tracking devices and/or camera traps. Despite the diversity of methods aimed at detecting contacts, the analysis of transmission risk is often reduced to contact rates and the probability of transmission given the contact. However, the latter process is continuous over time and unique for each contact, and is influenced by the characteristics of the contact and the pathogen's relationship with both the host and the environment. Our objective was to assess whether a more comprehensive approach, using a movement-based model which assigns a unique transmission risk to each contact by decomposing transmission into contact formation, contact duration and host characteristics, could reveal disease transmission dynamics that are not detected with more traditional approaches. The model was built from GPS-collar data from two management systems in Spain where animal tuberculosis (TB) circulates: a national park with extensively reared endemic cattle, and an area with extensive free-range pigs and cattle farms. In addition, we evaluated the effect of the GPS device fix rate on the performance of the model. Different transmission dynamics were identified between both management systems. Considering the specific conditions under which each contact occurs (i.e. whether the contact is direct or indirect, its duration, the hosts characteristics, the environmental conditions, etc.) resulted in the identification of different transmission dynamics compared to using only contact rates. We found that fix intervals greater than 30 min in the GPS tracking data resulted in missed interactions, and intervals greater than 2 h may be insufficient for epidemiological purposes. Our study shows that neglecting the conditions under which each contact occurs may result in a misidentification of the real role of each species in disease transmission. This study describes a clear and repeatable framework to study pathogen transmission from GPS data and provides further insights to understand how TB is maintained in multi-host systems in Mediterranean environments.

Spatiotemporally Explicit Epidemic Model for West Nile Virus Outbreak in Germany: An Inversely Calibrated Approach.

Since the first autochthonous transmission of West Nile Virus was detected in Germany (WNV) in 2018, it has become endemic in several parts of the country and is continuing to spread due to the attainment of a suitable environment for vector occurrence and pathogen transmission. Increasing temperature associated with a changing climate has been identified as a potential driver of mosquito-borne disease in temperate regions. This scenario justifies the need for the development of a spatially and temporarily explicit model that describes the dynamics of WNV transmission in Germany. In this study, we developed a process-based mechanistic epidemic model driven by environmental and epidemiological data. Functional traits of mosquitoes and birds of interest were used to parameterize our compartmental model appropriately. Air temperature, precipitation, and relative humidity were the key climatic forcings used to replicate the fundamental niche responsible for supporting mosquito population and infection transmission risks in the study area. An inverse calibration method was used to optimize our parameter selection. Our model was able to generate spatially and temporally explicit basic reproductive number (R0) maps showing dynamics of the WNV occurrences across Germany, which was strongly associated with the deviation from daily means of climatic forcings, signaling the impact of a changing climate in vector-borne disease dynamics. Epidemiological data for human infections sourced from Robert Koch Institute and animal cases collected from the Animal Diseases Information System (TSIS) of the Friedrich-Loeffler-Institute were used to validate model-simulated transmission rates. From our results, it was evident that West Nile Virus is likely to spread towards the western parts of Germany with the rapid attainment of environmental suitability for vector mosquitoes and amplifying host birds, especially short-distance migratory birds. Locations with high risk of WNV outbreak (Baden-Württemberg, Bavaria, Berlin, Brandenburg, Hamburg, North Rhine-Westphalia, Rhineland-Palatinate, Saarland, Saxony-Anhalt and Saxony) were shown on R0 maps. This study presents a path for developing an early warning system for vector-borne diseases driven by climate change.

Modeling different infectious phases of hepatitis B with generalized saturated incidence: An analysis and control.

Hepatitis B is one of the global health issues caused by the hepatitis B virus (HBV), producing 1.1 million deaths yearly. The acute and chronic phases of HBV are significant because worldwide, approximately 250 million people are infected by chronic hepatitis B. The chronic stage is a long-term, persistent infection that can cause liver damage and increase the risk of liver cancer. In the case of multiple phases of infection, a generalized saturated incidence rate model is more reasonable than a simply saturated incidence because it captures the complex dynamics of the different infection phases. In contrast, a simple saturated incidence rate model assumes a fixed shape for the incidence rate curve, which may not accurately reflect the dynamics of multiple infection phases. Considering HBV and its various phases, we constructed a model to present the dynamics and control strategies using the generalized saturated incidence. First, we proved that the model is well-posed. We then found the reproduction quantity and model equilibria to discuss the time dynamics of the model and investigate the conditions for stabilities. We also examined a control mechanism by introducing various controls to the model with the aim to increase the population of those recovered and minimize the infected people. We performed numerical experiments to check the biological significance and control implementation.

Development of the second version of Global Prediction System for Epidemiological Pandemic.

Coronavirus disease 2019 (COVID-19) is a severe global public health emergency that has caused a major crisis in the safety of human life, health, global economy, and social order. Moreover, COVID-19 poses significant challenges to healthcare systems worldwide. The prediction and early warning of infectious diseases on a global scale are the premise and basis for countries to jointly fight epidemics. However, because of the complexity of epidemics, predicting infectious diseases on a global scale faces significant challenges. In this study, we developed the second version of Global Prediction System for Epidemiological Pandemic (GPEP-2), which combines statistical methods with a modified epidemiological model. The GPEP-2 introduces various parameterization schemes for both impacts of natural factors (seasonal variations in weather and environmental impacts) and human social behaviors (government control and isolation, personnel gathered, indoor propagation, virus mutation, and vaccination). The GPEP-2 successfully predicted the COVID-19 pandemic in over 180 countries with an average accuracy rate of 82.7%. It also provided prediction and decision-making bases for several regional-scale COVID-19 pandemic outbreaks in China, with an average accuracy rate of 89.3%. Results showed that both anthropogenic and natural factors can affect virus spread and control measures in the early stages of an epidemic can effectively control the spread. The predicted results could serve as a reference for public health planning and policymaking.

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.

Long-term effects of non-pharmaceutical interventions on total disease burden in parsimonious epidemiological models.

The recent global COVID-19 pandemic resulted in governments enacting non-pharmaceutical interventions (NPIs) targeted at reducing transmission of SARS-CoV-2. But the NPIs also affected the transmission of viruses causing non-target seasonal respiratory diseases, including influenza and respiratory syncytial virus (RSV). In many countries, the NPIs were found to reduce cases of such seasonal respiratory diseases, but there is also evidence that subsequent relaxation of NPIs led to outbreaks of these diseases that were larger than pre-pandemic ones, due to the accumulation of susceptible individuals prior to relaxation. Therefore, the net long-term effects of NPIs on the total disease burden of non-target diseases remain unclear. Knowledge of this is important for infectious disease management and maintenance of public health. In this study, we shed light on this issue for the simplified scenario of a set of NPIs that prevent or reduce transmission of a seasonal respiratory disease for about a year and are then removed, using mathematical analyses and numerical simulations of a suite of four epidemiological models with varying complexity and generality. The model parameters were estimated using empirical data pertaining to seasonal respiratory diseases and covered a wide range. Our results showed that NPIs reduced the total disease burden of a non-target seasonal respiratory disease in the long-term. Expressed as a percentage of population size, the reduction was greater for larger values of the basic reproduction number and the immunity loss rate, reflecting larger outbreaks and hence more infections averted by imposition of NPIs. Our study provides a foundation for exploring the effects of NPIs on total disease burden in more-complex scenarios.

Parallel prediction of dengue cases with different risks in Mexico using an artificial neural network model considering meteorological data.

In 2022, Mexico registered an increase in dengue cases compared to the previous year. On the other hand, the amount of precipitation reported annually was slightly less than the previous year. Similarly, the minimum-mean-maximum temperatures recorded annually were below the previous year. In the literature, it is possible to find studies focused on the spread of dengue only for some specific regions of Mexico. However, given the increase in the number of cases during 2022 in regions not considered by previously published works, this study covers cases reported in all states of the country. On the other hand, determining a relationship between the dynamics of dengue cases and climatic factors through a computational model can provide relevant information on the transmission of the virus. A multiple-learning computational approach was developed to simulate the number of the different risks of dengue cases according to the classification reported per epidemiological week by considering climatic factors in Mexico. For the development of the model, the data were obtained from the reports published in the Epidemiological Panorama of Dengue in Mexico and in the National Meteorological Service. The classification of non-severe dengue, dengue with warning signs, and severe dengue were modeled in parallel through an artificial neural network model. Five variables were considered to train the model: the monthly average of the minimum, mean, and maximum temperatures, the precipitation, and the number of the epidemiological week. The selection of variables in this work is focused on the spread of the different risks of dengue once the mosquito begins transmitting the virus. Therefore, temperature and precipitation were chosen as climatic factors due to the close relationship between the density of adult mosquitoes and the incidence of the disease. The Levenberg-Marquardt algorithm was applied to fit the coefficients during the learning process. In the results, the ANN model simulated the classification of the different risks of dengue with the following precisions (R2): 0.9684, 0.9721, and 0.8001 for non-severe dengue, with alarm signs and severe, respectively. Applying a correlation matrix and a sensitivity analysis of the ANN model coefficients, both the average minimum temperature and precipitation were relevant to predict the number of dengue cases. Finally, the information discovered in this work can support the decision-making of the Ministry of Health to avoid a syndemic between the increase in dengue cases and other seasonal diseases.

A predator-prey fractional model with disease in the prey species.

In this paper, we study a generalized eco-epidemiological model of fractional order for the predator-prey type in the presence of an infectious disease in the prey. The proposed model considers that the disease infects the prey, causing them to be divided into two classes, susceptible prey and infected prey, with different density-dependent predation rates between the two classes. We propose logistic growth in both the prey and predator populations, and we also propose that the predators have alternative food sources (i.e., they do not feed exclusively on these prey). The model is evaluated from the perspective of the global and local generalized derivatives by using the generalized Caputo derivative and the generalized conformable derivative. The existence, uniqueness, non-negativity, and boundedness of the solutions of fractional order systems are demonstrated for the classical Caputo derivative. In addition, we study the stability of the equilibrium points of the model and the asymptotic behavior of its solution by using the Routh-Hurwitz stability criteria and the Matignon condition. Numerical simulations of the system are presented for both approaches (the classical Caputo derivative and the conformable Khalil derivative), and the results are compared with those obtained from the model with integro-differential equations. Finally, it is shown numerically that the introduction of a predator population in a susceptible-infectious system can help to control the spread of an infectious disease in the susceptible and infected prey population.

Impact of ontogenic changes on the dynamics of a fungal crop disease model motivated by coffee leaf rust.

Ontogenic resistance has been described for many plant-pathogen systems. Conversely, coffee leaf rust, a major fungal disease that drastically reduces coffee production, exhibits a form of ontogenic susceptibility, with a higher infection risk for mature leaves. To take into account stage-dependent crop response to phytopathogenic fungi, we developed an SEIR-U epidemiological model, where U stands for spores, which differentiates between young and mature leaves. Based on this model, we also explored the impact of ontogenic resistance on the sporulation rate. We computed the basic reproduction number [Formula: see text], which classically determines the stability of the disease-free equilibrium. We identified forward and backward bifurcation cases. The backward bifurcation is generated by the high sporulation of young leaves compared to mature ones. In this case, when the basic reproduction number is less than one, the disease can persist. These results provide useful insights on the disease dynamics and its control. In particular, ontogenic resistance may require higher control efforts to eradicate the disease.

Do Growers Using Solo Fungicides Affect the Durability of Disease Control of Growers Using Mixtures and Alternations? The Case of Spot-Form Net Blotch in Western Australia.

Growers often use alternations or mixtures of fungicides to slow down the development of resistance to fungicides. However, within a landscape, some growers will implement such resistance management methods, whereas others do not, and may even apply solo components of the resistance management program. We investigated whether growers using solo components of resistant management programs affect the durability of disease control in fields of those who implement fungicide resistance management. We developed a spatially implicit semidiscrete epidemiological model for the development of fungicide resistance. The model simulates the development of epidemics of spot-form net blotch disease, caused by the pathogen Pyrenophora teres f. maculata. The landscape comprises three types of fields, grouped according to their treatment program, with spore dispersal between fields early in the cropping season. In one field type, a fungicide resistance management method is implemented, whereas in the two others, it is not, with one of these field types using a component of the fungicide resistance management program. The output of the model suggests that the use of component fungicides does affect the durability of disease control for growers using resistance management programs. The magnitude of the effect depends on the characteristics of the pathosystem, the degree of inoculum mixing between fields, and the resistance management program being used. Additionally, although increasing the amount of the solo component in the landscape generally decreases the lifespan within which the resistance management program provides effective control, situations exist where the lifespan may be minimized at intermediate levels of the solo component fungicide. [Formula: see text] Copyright © 2024 The Author(s). This is an open access article distributed under the CC BY 4.0 International license.

Global prediction for mpox epidemic.

The mpox epidemic had spread worldwide and become an epidemic of international concern. Before the emergence of targeted vaccines and specific drugs, it is necessary to numerically simulate and predict the epidemic. In order to better understand and grasp its transmission situation, and take some countermeasures accordingly when necessary, we predicted and simulated mpox transmission, vaccination and control scenarios using model developed for COVID-19 predictions. The results show that the prediction model can also achieve good results in predicting the mpox epidemic based on modified SEIR model. The total number of people infected with mpox on Dec 31, 2022 reached 83878, while the prediction of the model was 96456 with a relative error of 15%. The United States, Brazil, Spain, France, the United Kingdom and Germany are six countries with serve mpox epidemic. The predictions of their epidemic are 30543, 11191, 7447, 5945, 5606 and 4291 cases respectively, with an average relative error of 20%. If 30% of the population is vaccinated using a vaccine that is 78% effective, the number of infected people will drop by 29%. This shows that the system can be practically applied to the prediction of mpox epidemic and provide corresponding decision-making reference.

Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants.

We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves.

An epidemiological model for analysing pandemic trends of novel coronavirus transmission with optimal control.

Symptomatic and asymptomatic individuals play a significant role in the transmission dynamics of novel Coronaviruses. By considering the dynamical behaviour of symptomatic and asymptomatic individuals, this study examines the temporal dynamics and optimal control of Coronavirus disease propagation using an epidemiological model. Biologically and mathematically, the well-posed epidemic problem is examined, as well as the threshold quantity with parameter sensitivity. Model parameters are quantified and their relative impact on the disease is evaluated. Additionally, the steady states are investigated to determine the model's stability and bifurcation. Using the dynamics and parameters sensitivity, we then introduce optimal control strategies for the elimination of the disease. Using real disease data, numerical simulations and model validation are performed to support theoretical findings and show the effects of control strategies.

Temporary Cross-Immunity as a Plausible Driver of Asynchronous Cycles of Dengue Serotypes.

Many infectious diseases exist as multiple variants, with interactions between variants potentially driving epidemiological dynamics. These diseases include dengue, which infects hundreds of millions of people every year and exhibits complex multi-serotype dynamics. Antibodies produced in response to primary infection by one of the four dengue serotypes can produce a period of temporary cross-immunity (TCI) to infection by other serotypes. After this period, the remaining antibodies can facilitate the entry of heterologous serotypes into target cells, thus enhancing severity of secondary infection by a heterologous serotype. This represents antibody-dependent enhancement (ADE). In this study, we analyze an epidemiological model to provide novel insights into the importance of TCI and ADE in producing cyclic outbreaks of dengue serotypes. Our analyses reveal that without TCI, such cyclic outbreaks are synchronous across serotypes and only occur when ADE produces high transmission rates. In contrast, the presence of TCI allows asynchronous cycles of serotypes by inducing a time lag between recovery from primary infection by one serotype and secondary infection by another, with such cycles able to occur without ADE. Our results suggest that TCI is a fundamental driver of asynchronous cycles of dengue serotypes and possibly other multi-variant diseases.

Epidemiological Model for Conventional Tobacco Control Measures and Tobacco Endgame Policies.

Epidemiological models, also known as host-agent-vector-environment models, are utilized in public health to gain insights into disease occurrence and to formulate intervention strategies. In this paper, we propose an epidemiological model that incorporates both conventional measures and tobacco endgame policies. Our model suggests that conventional measures focus on relationships among agent-vector-host-environment components, whereas endgame policies inherently aim to change or eliminate those components at a fundamental level. We also found that the vector (tobacco industry) and environment (physical and social surroundings) components were insufficiently researched or controlled by both conventional measures and tobacco endgame policies. The use of an epidemiological model for tobacco control and the tobacco endgame is recommended to identify areas that require greater effort and to develop effective intervention measures.

[Epidemiology and features of statistical accounting of in-hospital ischemic stroke (St. Petersburg experience)]. / Epidemiologiya i osobennosti statisticheskogo ucheta vnutrigospital'nogo ishemicheskogo insul'ta (na primere Sankt-Peterburga).

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.

Getting Jab or Regular Test: Observations from an Impulsive Epidemic COVID-19 Model.

Several safe and effective vaccines are available to prevent individuals from experiencing severe illness or death as a result of COVID-19. Widespread vaccination is widely regarded as a critical tool in the fight against the disease. However, some individuals may choose not to vaccinate due to vaccine hesitancy or other medical conditions. In some sectors, regular compulsory testing is required for such unvaccinated individuals. Interestingly, different sectors require testing at various frequencies, such as weekly or biweekly. As a result, it is essential to determine the optimal testing frequency and identify underlying factors. This study proposes a population-based model that can accommodate different personal decision choices, such as getting vaccinated or undergoing regular tests, as well as vaccine efficacies and uncertainties in epidemic transmission. The model, formulated as impulsive differential equations, uses time instants to represent the reporting date for the test result of an unvaccinated individual. By employing well-accepted indices to measure transmission risk, including the basic reproduction number, the peak time, the final size, and the number of severe infections, the study shows that an optimal testing frequency is highly sensitive to parameters involved in the transmission process, such as vaccine efficacy, disease transmission rate, test accuracy, and existing vaccination coverage. The testing frequency should be appropriately designed with the consideration of all these factors, as well as the control objectives measured by epidemiological quantities of great concern.

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.

Estimation of the size of the COVID-19 pandemic using the epidemiological wavelength model: results from OECD countries.

OBJECTIVES: This study aimed to simplify the previously developed epidemiological wavelength model and to expand the scope of the model with additional variables to estimate the magnitude of the COVID-19 pandemic. The applicability of the extended wavelength model was tested in Organisation for Economic Cooperation and Development (OECD) member countries. STUDY DESIGN: The epidemiological wavelengths of OECD member countries for the years 2020, 2021 and 2022 were estimated comparatively, considering the cumulative number of COVID-19 cases. METHODS: The size of the COVID-19 pandemic was estimated using the wavelength model. The scope of the wavelength model was expanded to include additional variables. The extended estimation model was improved by adding population density and human development index variables, in addition to the number of COVID-19 cases and number of days since the first case reported from the previous estimation model. RESULTS: According to the findings obtained from the wavelength model, the country with the highest epidemiological wavelength for the years 2020, 2021 and 2022 was the United States (We = 29.96, We = 28.63 and We = 28.86, respectively), and the country with the lowest wavelength was Australia (We = 10.50, We = 13.14 and We = 18.44, respectively). The average wavelength score of OECD member countries was highest in 2022 (We = 24.32) and lowest in 2020 (We = 22.84). The differences in the periodic wavelengths of OECD countries were analysed with the dependent t-test for paired samples in two periods, 2020-2021 and 2021-2022. There was a statistically significant difference between wavelengths in the 2020-2021 and 2021-2022 groups (t(36) = -3.670; P < 0.001). CONCLUSIONS: Decision-makers can use the extended wavelength model to easily follow the progress of the epidemic and to make quicker and more reliable decisions.