Mathematical Biosciences and Engineering

A discrete dynamic model for human epidemics was developed in present study. The model included major parameters as transmission strength and its decline parameters, mean incubation period, hospitalization time, non-hospitalization daily mortality, non-hospitalization daily recovery rate, and hospitalization proportion, etc. Sensitivity analysis of the model indicated the total cumulative cases significantly increased with initial transmission strength, hospitalization time. The total cumulative cases significantly decreased with transmission strengths decline and hospitalization proportion, and linearly decreased with non-hospitalization daily mortality and non-hospitalization daily recovery rate. In a certain range, the total cumulative cases significantly increased with mean incubation period. Sensitivity analysis demonstrated that dynamic change of transmission strength is one of the most important and controllable factors. In addition, reducing the delay for hospitalization is much effective in weakening disease epidemic. Non-hospitalization recovery rate is of importance for enhancing immunity to recover from the disease.

Moving infected animals and sharing contaminated vehicles are considered as the most potent ways for between-farm disease transmission. The objective of this study is to develop a network-based simulation model to investigate the effects of direct contact, indirect contact, and their combination on a hypothetical foot-and-mouth disease spreading between beef-cattle farms in southwest Kansas, US, and explore the effect of different types of information-sharing networks on preventing the disease spreading. Based on synthetic cattle and truck movement data in southwest Kansas, we build a farm-level contact network with three layers, a cattle movement layer (direct contact), a truck movement layer (indirect contact), and an information-sharing layer. Through scenario analyses, we compare the disease transmission dynamics, the distribution of outbreak epidemic size, and the disease breakout percentage of different contact structures - only direct contact, only indirect contact, and their combination. In addition, we evaluate different types of information sharing methods by comparing the epidemic size and the estimated economic loss. Simulation results show that neither direct contact nor indirect contact individually can result in a massive outbreak of the disease, but their combination plays a significant role. Additionally, we detect different probabilities of disease outbreaks by starting the simulations at different farms; starting at some farms with high capacity increases the probability of disease outbreaks. Three different information sharing-networks are developed and found effective in preventing the disease from spreading and reducing the economic loss. The information-sharing layer based on trading records has the best performance when compared with a random network and a geographic network.

BackgroundThe 2019 new coronavirus, "2019-nCoV", was discovered from Wuhan Viral Pneumonia cases in December 2019, and was named by the World Health Organization on January 12, 2020. In the early stage, people knows little about the 2019-nCoV virus was not clear, and the spread period was encountering Chinas annual spring migration, which made the epidemic spread rapidly from Wuhan to almost all provinces in China. MethodsThis study builds a SEIRD model that considers the movement of people across regions, revealing the effects of three measures on controlling the spread of the epidemic.Based on MATLAB R2017a, computational experiments were performed to simulate the epidemic prevention and control measures. FindingsThe research results show that current prevention and control measures in China are very necessary. This study further validates the concerns of international and domestic experts regarding asymptomatic transmission (E-status). InterpretationThe results of this study are applicable to explore the impact of the implementation of relevant measures on the prevention and control of epidemic spread, and to identify key individuals that may exist during the spread of the epidemic.

Antimicrobial resistance (AMR) is a serious threat to global health today. The spread of AMR, along with the lack of new drug classes in the antibiotic pipeline, has resulted in a renewed interest in phage therapy, which is the use of bacteriophages to treat pathogenic bacterial infections. This therapy, which was successfully used to treat a variety of infections in the early twentieth century, had been largely dismissed due to the discovery of easy to use antibiotics. However, the continuing emergence of antibiotic resistance has motivated new interest in the use of phage therapy to treat bacterial infections. Though various models have been developed to address the AMR-related issues, there are very few studies that consider the effect of phage-antibiotic combination therapy. Moreover, some of biological details such as the effect of the immune system on phage have been neglected. To address these limitations, we utilized a mathematical model to examine the role of the immune response in concert with phage-antibiotic combination therapy compounded with the effects of the immune system on the phages being used for treatment. We explore the effect of phage-antibiotic combination therapy by adjusting the phage and antibiotics dose or altering the timing. The model results show that it is important to consider the host immune system in the model and that frequency and dose of treatment are important considerations for the effectiveness of treatment. Our study can lead to development of optimal antibiotic use and further reduce the health risks of the human-animal-plant-ecosystem interface caused by AMR.

BackgroundExponential-like infection growths leading to peaks (which could be the inflection points or turning points) are usually the hallmarks of infectious disease outbreaks including coronaviruses. To predict the inflection points, i.e., inflection time (Tmax) & maximal infection number (Imax) of the novel coronavirus (COVID-19), we adopted a trial and error strategy and explored a series of approaches from simple logistic modeling (that has an asymptomatic line) to sophisticated tipping point detection techniques for detecting phase transitions but failed to obtain satisfactory results. MethodInspired by its success in diversity-time relationship (DTR), we apply the PLEC (power law with exponential cutoff) model for detecting the inflection points of COVID-19 outbreaks. The model was previously used to extend the classic species-time relationship (STR) for general DTR (Ma 2018), and it has two "secondary" parameters (computed from its 3 parameters including power law scaling parameter w, taper-off parameter d to overwhelm virtually exponential growth ultimately, and a parameter c related to initial infections): one that was originally used for estimating the potential or dark biodiversity is proposed to estimate the maximal infection number (Imax) and another is proposed to determine the corresponding inflection time point (Tmax). ResultsWe successfully estimated the inflection points [Imax, Tmax] for most provinces ({approx}85%) in China with error rates <5% in both Imax and Tmax. We also discussed the constraints and limitations of the proposed approach, including (i) sensitive to disruptive jumps, (ii) requiring sufficiently long datasets, and (iii) limited to unimodal outbreaks.

Livestock morbidity and death from Q-fever have been high, endangering local farmers livelihoods and affecting food security in Ghana. It is essential to understand the transmission dynamics of Q-fever to protect both the health of the animals and the main source of income for the community. A non-linear ordinary differential equation incorporating a vaccinated compartment was formulated and analyzed to gain insights into the spread of Q-fever. Routh Hurwitz criterion and Lyapunov function were used respectively to analyze the local and global stability of the disease-free equilibrium (Q0). We analyzed the behavior of the model compartments and discovered that many key factors significantly influence the persistence or eradication of Q-fever. Increased vaccination rates decrease the susceptible livestock while increasing the vaccinated livestock, potentially reducing the risk of outbreaks and limiting the spread of infections. A higher recovery rate leads to a quicker recovery, which aids in epidemic control by boosting population immunity and reducing the infectious time. The infection level rises when R0 > 1, indicating a typical transcritical bifurcation behavior, but this growth stays steady and does not result in unbounded advancement. Author summaryQ-fever presents considerable health hazards to livestock in Ghanas Tropical Savannah Grassland, adversely affecting local farmers income and food security in regions such as North Tongu municipality. To elucidate the transmission dynamics of the disease and safeguard both animal health and the communitys principal economic resource, we proposed a mathematical model employing non-linear differential equations that incorporate a vaccine compartment. This model enables the evaluation of how parameters such as vaccination and recovery rates influence the transmission of Q-fever in livestock. Our findings indicate that increased vaccination rates may diminish the population of susceptible livestock, hence reducing the possibility of outbreaks. In addition, a rapid recovery rate not only diminishes the duration of infectiousness in livestock but also enhances herd immunity, assisting in the containment of possible epidemics. The proposed model indicates that as R0 exceeds 1, the infection level rises, displaying transcritical bifurcation behavior. However, this rise stabilizes and prevents uncontrolled spread. These findings emphasize the value of vaccination and recovery techniques in controlling and possibly eliminating Q-fever in cattle, which would ultimately help Ghanaian farming communities remain sustainable.

Homeostasis is kind of force that makes living organism to live. In this study, we suggest an integral equation that models homeostasis in living organism. We also showed that various situations can be modeled by homeostasis, and give mathematical interpretation of mechanism of living organism. With our proposed integral equation, one can handle homeostasis quantitatively, and this approach is expected to unveil various hidden properties of living organism.

Plants growth is a complex and delicate balance among different factors involving environmental and physiological conditions. In this context, we propose a mechanistic model that considers the main internal processes of plant growth and reproduces a wide range of plant behaviors observed experimentally. In particular, we describe the model plant of Arabidopsis thaliana in a realistic environment with a day-and-night cycle, which considers different inputs as light, water, phosphorus, nitrogen, starch and sucrose. In addition, we propose a new function that describes the affinity between the plant and a specific nutrient, and a novel feedback signal to model how plants have the remarkable capacity to distribute resources among their organs. The result is an efficient tool applicable in ecological and agricultural studies, which can estimate several parameters, simulate several soil conditions and analyze how limiting or toxic resources can affect the plant development. We improve our understanding of plant adaptive strategies, reproducing results in line with experiments.

This study is based on the a simple but robust model we developed urgently to accurately monitor and predict viral dynamics for each SARS-CoV-2-infected patient, given the limited number of RT-PCR tests and the complexity of each individuals physical health situation. We used the mathematical model to monitor and predict the changes of viral loads from different nasal and throat swab of clinical specimens collected from diagnosed patients. We also tested this real-time model by using the data from the SARS-CoV-2-infected patients with different severity. By using this model (http://58.87.113.187:8080/), we can predict the viral dynamics of patients, minimize false-negative test results, and screen the patients who are at risk of testing positive again after recovery. We sincerely thank those who are on the front lines battling SARS-CoV-2 virus. We hope this model will be useful for SARS-CoV-2-infected patients.

Accurate prediction of the temporal and spatial characteristics of COVID-19 infection can provide favorable guidance for epidemic prevention and control. We first introduce individual antibody dynamics into an agent-based model. Antibody dynamics model can well explain the antibody fading effects through time. Based on this model, we further developed an agent-based approach which considers the dynamic behaviors of each individual antibodies. The method can effectively reflect the dynamic interaction between the antibody and the virus in each host body in the overall population. Using this method, we can accurately predict the temporal and spatial characteristics of the epidemic. It can quantitatively calculate the number and spatial distribution of infected persons with different symptoms at different times. At the same time, our model can predict the prevention and control effect of different prevention and control measures. At present, Chinas dynamic zero strategies mainly include large-scale nucleic acid test, isolation of positive infected persons and their close contacts. Our model demonstrates that for a less infectious and more virulent variant, this approach can achieve good preventive effect. The effect of reducing social contacts and quarantining only positive infected persons is relatively weaker on epidemic control. This can explain why Chinas targeted epidemic-control measures had an excellent performance in 2020 and 2021. However, our model also warns that for the highly infectious and less virulent variant, targeted epidemic-control measures can no longer achieve effective control of the epidemic. Therefore, we must choose to quarantine potential infected groups in a wider range (such as the quarantine of secondary close contact and tertiary close contact) or coexist with the virus. Furthermore, our model has a strong traceability ability, which can effectively conduct epidemiological investigation to unearth patient number zero based on the early epidemic distribution. In the end, our model expands the traditional approaches of epidemiological simulation and provides an alternative in epidemic modeling. Major findingsFirst, a method was developed to integrate the characteristics of individual antibody dynamics into epidemic prediction; Second, this model can effectively predict the spatiotemporal characteristics of patients with different symptoms (including asymptomatic patients, mild and severe patients, etc.); Thirdly, this model proves that Chinas dynamic zero strategy which include the quarantine of close contact people is more efficient than just isolating positive cases; Fourth: This model also reflects the limitations of targeted epidemic-control strategies and warns that for the highly infectious and less virulent variant, targeted epidemic-control measures can no longer achieve effective control of the epidemic; Fifth, this model can help epidemiological research and find out patient zero according to the early incidence of the epidemic.

During the coronavirus disease 2019 (COVID-19) outbreak, every public health system faced the potential challenge of medical capacity shortages. Infections without timely diagnosis or treatment may facilitate the stealth transmission and spread of the virus. Using infection and medical capacity information reported in Wuhan in China, New York State in the United States, and Italy, we developed a dynamic susceptible-exposed-infected-recovered (SEIR) model to estimate the impact of medical capacity shortages during the COVID-19 outbreak at the city, state, and country levels. After accounting for the effects of travel restrictions and control measures, we find that the number of infections in Wuhan could have been 39% lower than the actual number if the medical capacity were doubled in this city. Similarly, we find the less shortages in medical capacity in both New York state and Italy, the faster decline in the daily infection numbers and the fewer deaths. This study provides a method for estimating potential shortages and explains how they may dynamically facilitate disease spreading during future pandemics such as COVID-19.

Therapeutic vaccines are used to boost patients immune system activity by imposing signals that increase T cell proliferation or infiltration. A large population of cytotoxic T cells may then be able to reduce tumor growth. We developed here a mathematical model of vaccine-induced immunotherapy and used it to test the vaccine frequency and doses that can reduce tumor burden. Since tumors are heterogeneous, we examined if the proposed treatments are robust; i.e, are successful for a wide range of tumors. This was assessed by constructing virtual mice cohorts. Together, the optimal and most robust treatment protocol was determined through mathematical modeling.

Thermoregulation is crucial to homeostasis, but the mechanisms of its dysfunction are still largely mysterious, including fever, which is generally the most disconcerting sign of a serious infection or disease. Theories on body temperature dynamics that aim to explain a fever, such as changes in an internal setpoint, have been proposed, but none can identify the fundamental molecular pathways that produce a fever. Here, potential molecular pathways resultant in fever are identified, modeled, and compared to experimental temperature response data. Based on recent developments made by this lab, which has shown that the pyrogen prostaglandin E2 (PGE2) possesses similar binding affinity as the hormone cortisol (CORT) at the critical ligand binding domain (LBD) of glucocorticoid receptors (GR); molecular modeling, mathematical modeling and a case study for validation is used to indicate that competitive inhibition of CORT by PGE2 as a fundamental reason for dysfunctional dynamics of body temperature, including fever. Comprised of a superposition of proportional and derivative terms of signals representing temperature receptors, CORT concentration, and PGE2 concentration, the internal temperature control model characterizes dynamics associated with the cardiovascular, immune, and neural systems in response to infectious agents, triggering events, and other causal factors. The model is validated by examination of the transient and spectral characteristics of a three-day case history involving temperature trajectories after physical activity protocols in response to a standard vaccination of pneumococcal and influenza species.

Adaptive immunity plays a crucial role in defending against invading pathogenic microorganisms. It encompasses both humoral and cellular immune responses. For the first time, we have systematically developed a mathematical model of adaptive immunity that comprehensively incorporates the effects of both humoral and cellular immunity. Our model successfully explains several key immunological phenomena, including the formation of immune memory (involving both B-cell and T-cell memory), the mechanism of original antigenic sin, the basis of secondary infections, and the processes of activation and exhaustion in cellular immunity. Furthermore, we employed a discrete time-scale agent-based modeling approach to simulate the dynamics of the adaptive immune response following pathogen invasion, with a specific focus on elucidating the mechanisms underlying chronic infection. Finally, we have established a novel mathematical model of the interaction between cancer cells and the immune system, providing a more robust theoretical foundation for cancer immunotherapy.

The An-E-gs model, which consistently describes leaf photosynthesis (An), transpiration (E), and stomatal conductance (gs), is widely recognized and utilized as a "standard model" for quantifying these processes in terrestrial plants. However, since its proposal over 30 years ago, the model has faced a longstanding challenge: the "solution selection" problem, arising from the existence of multiple solutions with no guarantee that the obtained solution is correct. In this study, we mathematically proved that the An-E-gs model always has a unique solution satisfying the criteria gs > 0 and Ci > 0, where Ci represents the CO2 concentration inside the leaf. This result establishes a rigorous mathematical theorem on the existence and uniqueness of solutions in the model. The theorem resolves the longstanding "solution selection" problem by enabling the unambiguous identification of the correct solution through selecting the unique solution that satisfies these criteria. Furthermore, the theorem ensures the validity of past estimations that satisfy these criteria and guarantees that future studies applying these criteria will yield correct estimations. These findings provide a robust mathematical foundation for the An-E-gs model, reinforcing its role as the standard model for estimating leaf photosynthesis, transpiration, and stomatal conductance across diverse disciplines, from plant biology to climate science and beyond.

Mathematical modeling is a process aimed at finding a mathematical description of a system and translating it into a relational expression. When a system is continuously changing over time (e.g., infectious diseases) differential equations, which may include parameters, are used for modeling the system. The process of finding those parameters that best fit the given data from the system is called an inverse problem. This study aims at analyzing the novel coronavirus infection (COVID-19) spread in South Korea using the susceptible-infected-recovered (SIR) model. We collect the data from Korea Centers for Disease Control & Prevention (KCDC). We assume that each parameter in the SIR model is a function of time so that we can compute important parameters, such as the basic reproduction number (R0), more delicately. Using neural networks, we propose a method to find the best time-varying parameters and the solution for the model simultaneously. Moreover, using time-dependent parameters, we find that traditional numerical algorithms, such as the Runge-Kutta methods, can successfully approximate the SIR model while fitting the COVID-19 data, thus modeling the propagation patterns of COVID-19 more precisely.

The bacterium Xylella fastidiosa (Xf) is mainly transmitted by the spittlebug, Philaenus spumarius, in Europe, where it has caused significant economic damage to olive and almond trees. Understanding the factors that determine disease dynamics in pathosystems that share similarities can help design control strategies focused on minimizing transmission chains. Here we introduce a compartmental model for Xf-caused diseases in Europe that accounts for the main relevant epidemiological processes, including the seasonal dynamics of P. spumarius. The model was confronted with epidemiological data from the two major outbreaks of Xf in Europe, the olive quick disease syndrome (OQDS) in Apulia, Italy, caused by the subspecies pauca, and the almond leaf scorch disease (ALSD) in Majorca, Spain, caused by subspecies multiplex and fastidiosa. Using a Bayesian inference framework, we show how the model successfully reproduces the general field data in both diseases. In a global sensitivity analysis, the vector-plant and plant-vector transmission rates, together with the vector removal rate, were the most influential parameters in determining the time of the infected host population peak, the incidence peak and the final number of dead hosts. We also used our model to check different vector-based control strategies, showing that a joint strategy focused on increasing the rate of vector removal while lowering the number of annual newborn vectors is optimal for disease control.

Usutu virus is an emerging mosquito-borne flavivirus, maintained through an enzootic cycle involving wild birds and mosquitoes, with occasional spillover to humans. Understanding how interactions across these biological scales shape transmission dynamics is essential for predicting outbreaks and improving surveillance strategies. In this study, we developed a multiscale vector-borne model of Usutu virus infection that links within-host viral kinetics in birds, the per-bite probability of mosquito infection, and population-level mosquito-bird transmission dynamics. Model parameters were validated using two laboratory datasets collected under an optimally designed experimental framework and one surveillance dataset from wild bird populations. Structural and practical identifiability analyses were conducted to evaluate parameter robustness under varying levels of measurement noise. We found that simultaneous multiscale fitting to integrated datasets improved parameter identifiability and robustness. These results highlight the importance of combining microscale and macroscale data to enhance the predictive reliability of vector-borne disease models and demonstrate the broader utility of multiscale modeling frameworks for understanding the transmission dynamics of emerging arboviruses. Author summaryIn this study, we developed a multiscale vector-borne model of Usutu virus infection and validated its parameters using both laboratory data collected under an optimally designed experimental framework and published surveillance data from wild bird populations. Using this model, we quantified the robustness of parameter estimates and found that multiscale fitting to integrated datasets improves the reliability and identifiability of model parameters. The results highlight the importance of combining microscale and macroscale data to enhance the predictive reliability of vector-borne disease models.

Weeds present a major challenge to agricultural productivity, competing with crops for critical resources like water, nutrients, and sunlight, resulting in significant yield reductions. Prompt weed identification is essential for enabling effective control strategies, such as the application of herbicides or mechanical removal, to minimize their impact on crop growth. This research focuses on developing a deep learning approach based on game theory for detecting weeds. Using CWFID dataset captured at various times and days, along with multispectral data in the visible and near-infrared spectrum, the study aims to improve early detection methods for more efficient weed management in agricultural settings. A novel segmentation technique for weed regions is introduced, employing a zero-sum game theory model to reconcile conflicting classifications from different weed detectors. These regions are treated as zones of conflict between weeds and crops, with each detector representing a different strategy. By defining an appropriate utility function, the method identifies the Nash equilibrium, effectively minimizing false positive detections of weeds.

In this article, we conduct a literature review on the history and mathematical modeling of infectious diseases and COVID-19. Next, some simple epidemic dynamic models and the basic reproductive number theory are introduced. We propose a SEIDR model for COVID-19 and provide the solution methods for the basic reproduction number, parameters, and dynamic model. Finally, we simulate the early stages of the COVID-19 epidemic in Argentina, Indonesia, Mexico, and South Africa with the SEIDR model.