Mathematical Biosciences and Engineering最新文献

We modeled the impact of local vaccine mandates on the spread of vaccine-preventable infectious diseases, which in the absence of vaccines will mainly affect children. Examples of such diseases are measles, rubella, mumps, and pertussis. To model the spread of the pathogen, we used a stochastic SIR (susceptible, infectious, recovered) model with two levels of mixing in a closed population, often referred to as the household model. In this model, individuals make local contacts within a specific small subgroup of the population (e.g., within a household or a school class), while they also make global contacts with random people in the population at a much lower rate than the rate of local contacts. We considered what would happen if schools were given freedom to impose vaccine mandates on all of their pupils, except for the pupils that were exempt from vaccination because of medical reasons. We investigated first how such a mandate affected the probability of an outbreak of a disease. Furthermore, we focused on the probability that a pupil that was medically exempt from vaccination, would get infected during an outbreak. We showed that if the population vaccine coverage was close to the herd-immunity level, then both probabilities may increase if local vaccine mandates were implemented. This was caused by unvaccinated pupils possibly being moved to schools without mandates.

Respiratory diseases represent one of the most significant economic burdens on healthcare systems worldwide. The variation in the increasing number of cases depends greatly on climatic seasonal effects, socioeconomic factors, and pollution. Therefore, understanding these variations and obtaining precise forecasts allows health authorities to make correct decisions regarding the allocation of limited economic and human resources. We aimed to model and forecast weekly hospitalizations due to respiratory conditions in seven regional hospitals in Costa Rica using four statistical learning techniques (Random Forest, XGboost, Facebook's Prophet forecasting model, and an ensemble method combining the above methods), along with 22 climate change indices and aerosol optical depth as an indicator of pollution. Models were trained using data from 2000 to 2018 and were evaluated using data from 2019 as testing data. During the training period, we set up 2-year sliding windows and a 1-year assessment period, along with the grid search method to optimize hyperparameters for each model. The best model for each region was selected using testing data, based on predictive precision and to prevent overfitting. Prediction intervals were then computed using conformal inference. The relative importance of all climatic variables was computed for the best model, and similar patterns in some of the seven regions were observed based on the selected model. Finally, reliable predictions were obtained for each of the seven regional hospitals.

After the many failures in the control of the COVID-19 pandemic, identifying robust principles of epidemic control will be key in future preparedness. In this work, we propose an optimal control model of an age-of-infection transmission model under a two-phase control regime where social distancing is the only available control tool in the first phase, while the second phase also benefits from the arrival of vaccines. We analyzed the problem by an ad-hoc numerical algorithm under a strong hypothesis implying a high degree of prioritization to the protection of health from the epidemic attack, which we termed the "low attack rate" hypothesis. The outputs of the model were also compared with the data from the Italian COVID-19 experience to provide a crude assessment of the goodness of the enacted interventions prior to the onset of the Omicron variant.

Bike-sharing systems (BSSs) have become commonplace in most cities worldwide as an important part of many smart cities. These systems generate a continuous amount of large data volumes. The effectiveness of these BSS systems depends on making decisions at the proper time. Thus, there is a vital need to build predictive models on the BSS data for the sake of improving the process of decision-making. The overwhelming majority of BSS users register before utilizing the service. Thus, several BSSs have prior knowledge of the user's data, such as age, gender, and other relevant details. Several machine learning and deep learning models, for instance, are used to predict urban flows, trip duration, and other factors. The standard practice for these models is to train on the entire dataset to build a predictive model, whereas the biking patterns of various users are intuitively distinct. For instance, the user's age influences the duration of a trip. This endeavor was motivated by the existence of distinct user patterns. In this work, we proposed divide-and-train, a new method for training predictive models on station-based BSS datasets by dividing the original datasets on the values of a given dataset attribute. Then, the proposed method was validated on different machine learning and deep learning models. All employed models were trained on both the complete and split datasets. The enhancements made to the evaluation metric were then reported. Results demonstrated that the proposed method outperformed the conventional training approach. Specifically, the root mean squared error (RMSE) and mean absolute error (MAE) metrics have shown improvements in both trip duration and distance prediction, with an average accuracy of 85% across the divided sub-datasets for the best performing model, i.e., random forest.

A new mathematical model for the transmission dynamics and control of the Middle Eastern respiratory syndrome (MERS), a respiratory virus caused by MERS-CoV coronavirus (and primarily spread to humans by dromedary camels) that first emerged out of the Kingdom of Saudi Arabia (KSA) in 2012, was designed and used to study the transmission dynamics of the disease in a human-camel population within the KSA. Rigorous analysis of the model, which was fitted and cross-validated using the observed MERS-CoV data for the KSA, showed that its disease-free equilibrium was locally asymptotically stable whenever its reproduction number (denoted by $ {mathbb R}_{0M} $) was less than unity. Using the fixed and estimated parameters of the model, the value of $ {mathbb R}_{0M} $ for the KSA was estimated to be 0.84, suggesting that the prospects for MERS-CoV elimination are highly promising. The model was extended to allow for the assessment of public health intervention strategies, notably the potential use of vaccines for both humans and camels and the use of face masks by humans in public or when in close proximity with camels. Simulations of the extended model showed that the use of the face mask by humans who come in close proximity with camels, as a sole public health intervention strategy, significantly reduced human-to-camel and camel-to-human transmission of the disease, and this reduction depends on the efficacy and coverage of the mask type used in the community. For instance, if surgical masks are prioritized, the disease can be eliminated in both the human and camel population if at least 45% of individuals who have close contact with camels wear them consistently. The simulations further showed that while vaccinating humans as a sole intervention strategy only had marginal impact in reducing the disease burden in the human population, an intervention strategy based on vaccinating camels only resulted in a significant reduction in the disease burden in camels (and, consequently, in humans as well). Thus, this study suggests that attention should be focused on effectively combating the disease in the camel population, rather than in the human population. Furthermore, the extended model was used to simulate a hybrid strategy, which combined vaccination of both humans and camels as well as the use of face masks by humans. This simulation showed a marked reduction of the disease burden in both humans and camels, with an increasing effectiveness level of this intervention, in comparison to the baseline scenario or any of the aforementioned sole vaccination scenarios. In summary, this study showed that the prospect of the elimination of MERS-CoV-2 in the Kingdom of Saudi Arabia is promising using pharmaceutical (vaccination) and nonpharmaceutical (mask) intervention strategies, implemented in isolation or (preferably) in combination, that are focused on reducing the disease burden in the camel population.

This research focused its interest on the mathematical modeling of the demographic dynamics of semelparous biological species through branching processes. We continued the research line started in previous papers, providing new methodological contributions of biological and ecological interest. We determined the probability distribution associated with the number of generations elapsed before the possible extinction of the population in its natural habitat. We mathematically modeled the phenomenon of populating or repopulating habitats with semelparous species. We also proposed estimates for the offspring parameters governing the reproductive strategies of the species. To this purpose, we used the maximum likelihood and Bayesian estimation methodologies. The statistical results are illustrated through a simulated example contextualized with Labord chameleon (Furcifer labordi) species.

For numerous viruses, their capsid assembly is composed of two steps. The first step is that virus structural protein monomers are polymerized to building blocks. Then, these building blocks are cumulative and efficiently assembled to virus capsid shell. These building block polymerization reactions in the first step are fundamental for virus assembly, and some drug targets were found in this step. In this work, we focused on the first step. Often, virus building blocks consisted of less than six monomers. That is, dimer, trimer, tetramer, pentamer, and hexamer. We presented mathematical models for polymerization chemical reactions of these five building blocks, respectively. Then, we proved the existence and uniqueness of the positive equilibrium solution for these mathematical models one by one. Subsequently, we also analyzed the stability of the equilibrium states, respectively. These results may provide further insight into property of virus building block polymerization chemical reactions in vivo.

The pursuit of effective vaccination strategies against COVID-19 remains a critical endeavour in global public health, particularly amidst challenges posed by immunity loss and evolving epidemiological dynamics. This study investigated optimal vaccination strategies by considering age structure, immunity dynamics, and varying maximal vaccination rates. To this end, we formulated an SEIR model stratified into $ n $ age classes, with the vaccination rate as an age-dependent control variable in an optimal control problem. We developed an objective function aimed at minimising critical infections while optimising vaccination efforts and then conducted rigorous mathematical analyses to ensure the existence and characterization of the optimal control. Using data from three countries with diverse age distributions, in expansive, constrictive, and stationary pyramids, we performed numerical simulations to evaluate the optimal age-dependent vaccination strategy, number of critical infections, and vaccination frequency. Our findings highlight the significant influence of maximal vaccination rates on shaping optimal vaccination strategies. Under constant maximal vaccination rates, prioritising age groups based on population demographics proves effective, with higher rates resulting in fewer critically infected individuals across all age distributions. Conversely, adopting age-dependent maximal vaccination rates, akin to the WHO strategy, may not always lead to the lowest critical infection peaks but offers a viable alternative in resource-constrained settings.