A study of integrated pest management models with instantaneous and non-instantaneous impulse effects

The occurrence of pests and diseases during agricultural production affects the quality and quantity of agricultural products. It is important to evaluate the impact of various factors on pests to achieve optimal results of integrated pest management (IPM) during its implementation. In this paper, we considered the transient and non-transient effects of chemical control on pests and the effects on natural enemies at different times, and developed a corresponding pest control model. Detailed studies and comparisons were conducted for spraying pesticides either more or less frequently as compared to strategies for releasing natural enemies. The threshold conditions for global asymptotic stabilization of the pest extinction period solution was obtained. Using two-parameter and sensitivity analysis techniques, the parameters affecting the variation of the threshold were discussed. By comparing these two pest control strategies, we found the existence of optimal application and release frequencies. Finally, in order to control pests below the economic threshold level, the state-dependent pest model was numerically investigated. The results show that the presence or absence of chemical control of pests can depend on the values taken for the parameters in the model. Based on this information, pest control experts can make decisions about the best spraying time and the best release rate.

Qualitative behavior of a highly non-linear Cutaneous Leishmania epidemic model under convex incidence rate with real data

In the context of this investigation, we introduce an innovative mathematical model designed to elucidate the intricate dynamics underlying the transmission of Anthroponotic Cutaneous Leishmania. This model offers a comprehensive exploration of the qualitative characteristics associated with the transmission process. Employing the next-generation method, we deduce the threshold value $ R_0 $ for this model. We rigorously explore both local and global stability conditions in the disease-free scenario, contingent upon $ R_0 $ being less than unity. Furthermore, we elucidate the global stability at the disease-free equilibrium point by leveraging the Castillo-Chavez method. In contrast, at the endemic equilibrium point, we establish conditions for local and global stability, when $ R_0 $ exceeds unity. To achieve global stability at the endemic equilibrium, we employ a geometric approach, a Lyapunov theory extension, incorporating a secondary additive compound matrix. Additionally, we conduct sensitivity analysis to assess the impact of various parameters on the threshold number. Employing center manifold theory, we delve into bifurcation analysis. Estimation of parameter values is carried out using least squares curve fitting techniques. Finally, we present a comprehensive discussion with graphical representation of key parameters in the concluding section of the paper.

Nonlinear dynamics of estrogen receptor-positive breast cancer integrating experimental data: A novel spatial modeling approach

Oncology research has focused extensively on estrogen hormones and their function in breast cancer proliferation. Mathematical modeling is essential for the analysis and simulation of breast cancers. This research presents a novel approach to examine the therapeutic and inhibitory effects of hormone and estrogen therapies on the onset of breast cancer. Our proposed mathematical model comprises a nonlinear coupled system of partial differential equations, capturing intricate interactions among estrogen, cytotoxic T lymphocytes, dormant cancer cells, and active cancer cells. The model's parameters are meticulously estimated through experimental studies, and we conduct a comprehensive global sensitivity analysis to assess the uncertainty of these parameter values. Remarkably, our findings underscore the pivotal role of hormone therapy in curtailing breast tumor growth by blocking estrogen's influence on cancer cells. Beyond this crucial insight, our proposed model offers an integrated framework to delve into the complexity of tumor progression and immune response under hormone therapy. We employ diverse experimental datasets encompassing gene expression profiles, spatial tumor morphology, and cellular interactions. Integrating multidimensional experimental data with mathematical models enhances our understanding of breast cancer dynamics and paves the way for personalized treatment strategies. Our study advances our comprehension of estrogen receptor-positive breast cancer and exemplifies a transformative approach that merges experimental data with cutting-edge mathematical modeling. This framework promises to illuminate the complexities of cancer progression and therapy, with broad implications for oncology.

Modelling and analysis of the HIV/AIDS epidemic with fast and slow asymptomatic infections in China from 2008 to 2021

The aim of this paper is to investigate the spread of the HIV/AIDS epidemic in China during 2008-2021. A new mathematical model is proposed to study the dynamics of HIV transmission with acute infection, fast asymptomatic infections, and slow asymptomatic infections. The basic reproduction number is obtained by the next-generation matrix method. A quantitative analysis of the model, including the local behavior, global behavior, and permanence, is performed. Numerical simulations are presented to enhance the results of these analyses. The behavior or the model's parameters are estimated from real data. A sensitivity analysis shows that the proportion of asymptomatic infections co-infected with other diseases significantly affects the basic reproduction number. We further analyze the impact of implementing single and multiple measure(s) in parallel with the epidemic. The study results conclude that multiple measures are more effective in controlling the spread of AIDS compared to just one. The HIV epidemic can be effectively curbed by reducing the contact rate between fast asymptomatic infected individuals and susceptible populations, increasing the early diagnosis and screening of HIV-infected individuals co-infected with other diseases, and treating co-infected patients promptly.

Analysis of the current status of TB transmission in China based on an age heterogeneity model

Tuberculosis (TB) is an infectious disease transmitted through the respiratory system. China is one of the countries with a high burden of TB. Since 2004, an average of more than 800,000 cases of active TB has been reported each year in China. Analyzing the case data from 2004 to 2018, we found significant differences in TB incidence by age group. A model of TB is put forward to explore the effect of age heterogeneity on TB transmission. The nonlinear least squares method is used to obtain the key parameters in the model, and the basic reproduction number Rv = 0.8017 is calculated and the sensitivity analysis of Rv to the parameters is given. The simulation results show that reducing the number of new infections in the elderly population and increasing the recovery rate of elderly patients with the disease could significantly reduce the transmission of TB. Furthermore, the feasibility of achieving the goals of the World Health Organization (WHO) End TB Strategy in China is assessed, and we obtained that with existing TB control measures it will take another 30 years for China to reach the WHO goal to reduce 90% of the number of new cases by the year 2049. However, in theory it is feasible to reach the WHO strategic goal of ending TB by 2035 if the group contact rate in the elderly population can be reduced, though it is difficult to reduce the contact rate.

Dynamics analysis of strangles with asymptomatic infected horses and long-term subclinical carriers

Strangles is one of the most prevalent horse diseases globally. The infected horses may be asymptomatic and can still carry the infectious pathogen after it recovers, which are named asymptomatic infected horses and long-term subclinical carriers, respectively. Based on these horses, this paper establishes a dynamical model to screen, measure, and model the spread of strangles. The basic reproduction number $ \mathcal{R}_0 $ is computed through a next generation matrix method. By constructing Lyapunov functions, we concluded that the disease-free equilibrium is globally asymptotically stable if $ \mathcal{R}_0 < 1 $, and the endemic equilibrium exits uniquely and is globally asymptotically stable if $ \mathcal{R}_0 > 1 $. For example, while studying a strangles outbreak of a horse farm in England in 2012, we computed an $ \mathcal{R}_0 = 0.8416 $ of this outbreak by data fitting. We further conducted a parameter sensitivity analysis of $ \mathcal{R}_0 $ and the final size by numerical simulations. The results show that the asymptomatic horses mainly influence the final size of this outbreak and that long-term carriers are connected to an increased recurrence of strangles. Moreover, in terms of the three control measures implemented to control strangles(i.e., vaccination, implementing screening regularly and isolating symptomatic horses), the result shows that screening is the most effective measurement, followed by vaccination and isolation, which can provide effective guidance for horse management.

Modeling and analysis of the transmission dynamics of cystic echinococcosis: Effects of increasing the number of sheep

A transmission dynamics model with the logistic growth of cystic echinococcus in sheep was formulated and analyzed. The basic reproduction number was derived and the results showed that the global dynamical behaviors were determined by its value. The disease-free equilibrium is globally asymptotically stable when the value of the basic reproduction number is less than one; otherwise, there exists a unique endemic equilibrium and it is globally asymptotically stable. Sensitivity analysis and uncertainty analysis of the basic reproduction number were also performed to screen the important factors that influence the spread of cystic echinococcosis. Contour plots of the basic reproduction number versus these important factors are presented, too. The results showed that the higher the deworming rate of dogs, the lower the prevalence of echinococcosis in sheep and dogs. Similarly, the higher the slaughter rate of sheep, the lower the prevalence of echinococcosis in sheep and dogs. It also showed that the spread of echinococcosis has a close relationship with the maximum environmental capacity of sheep, and that they have a remarkable negative correlation. This reminds us that the risk of cystic echinococcosis may be underestimated if we ignore the increasing number of sheep in reality.

Dynamics of an SEIR model with media coverage mediated nonlinear infectious force

Media coverage can greatly impact the spread of infectious diseases. Taking into consideration the impacts of media coverage, we propose an SEIR model with a media coverage mediated nonlinear infection force. For this novel disease model, we identify the basic reproduction number using the next generation matrix method and establish the global threshold results: If the basic reproduction number $ \mathcal{R}_{0} < 1 $, then the disease-free equilibrium $ P_{0} $ is stable, and the disease dies out. If $ \mathcal{R}_{0} > 1 $, then the endemic equilibrium $ P^{*} $ is stable, and the disease persists. Sensitivity analysis indicates that the basic reproduction number $ \mathcal{R}_{0} $ is most sensitive to the population recruitment rate $ \Lambda $ and the disease transmission rate $ \beta _{1} $.

Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number ($ \mathcal{R}_{0} $) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of $ \mathcal{R}_{0} $ to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time-dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.

Simulations and fractional modeling of dengue transmission in Bangladesh

Dengue is one of the most infectious diseases in the world. In Bangladesh, dengue occurs nationally and has been endemic for more than a decade. Therefore, it is crucial that we model dengue transmission in order to better understand how the illness behaves. This paper presents and analyzes a novel fractional model for the dengue transmission utilizing the non-integer Caputo derivative (CD) and are analysed using q-homotopy analysis transform method (q-HATM). By using the next generation method, we derive the fundamental reproduction number $ R_0 $ and show the findings based on it. The global stability of the endemic equilibrium (EE) and the disease-free equilibrium (DFE) is calculated using the Lyapunov function. For the proposed fractional model, numerical simulations and dynamical attitude are seen. Moreover, A sensitivity analysis of the model is performed to determine the relative importance of the model parameters to the transmission.

A mechanistic mathematical model for photo fermentative hydrogen and polyhydroxybutyrate production

An original mathematical model describing the photo fermentation process is proposed. The model represents the first attempt to describe the photo fermentative hydrogen production and polyhydroxybutyrate accumulation, simultaneously. The mathematical model is derived from mass balance principles and consists of a system of ordinary differential equations describing the biomass growth, the nitrogen and the substrate degradation, the hydrogen and other catabolites production, and the polyhydroxybutyrate accumulation in photo fermentation systems. Moreover, the model takes into account important inhibiting phenomena, such as the self-shading and the substrate inhibition, which can occur during the evolution of the process. The calibration was performed using a real experimental data set and it was supported by the results of a sensitivity analysis study. The results showed that the most sensitive parameters for both hydrogen and PHB production were the hydrogen yield on substrate, the catabolites yield on substrate, and the biomass yield. Successively, a different experimental data set was used to validate the model. Performance indicators showed that the model could efficiently be used to simulate the photo fermentative hydrogen and polyhydroxybutyrate production by Rhodopseudomonas palustris. For instance, the index of agreement of 0.95 was observed for the validated hydrogen production trend. Moreover, the model well predicted the maximum PHB accumulation in bacterial cells. Indeed, the predicted and observed accumulated PHB were 4.5 and 4.8%, respectively. Further numerical simulations demonstrated the model consistency in describing process inhibiting phenomena. Numerical simulations showed that the acetate and nitrogen inhibition phenomena take place when concentrations are higher than 12.44 g L^-1 and lower than 4.76 mg L^-1, respectively. Finally, the potential long term hydrogen production from accumulated polyhydroxybutyrate in bacterial cells was studied via a fast-slow analysis technique.

Evaluating the impact of multiple factors on the control of COVID-19 epidemic: A modelling analysis using India as a case study

The currently ongoing COVID-19 outbreak remains a global health concern. Understanding the transmission modes of COVID-19 can help develop more effective prevention and control strategies. In this study, we devise a two-strain nonlinear dynamical model with the purpose to shed light on the effect of multiple factors on the outbreak of the epidemic. Our targeted model incorporates the simultaneous transmission of the mutant strain and wild strain, environmental transmission and the implementation of vaccination, in the context of shortage of essential medical resources. By using the nonlinear least-square method, the model is validated based on the daily case data of the second COVID-19 wave in India, which has triggered a heavy load of confirmed cases. We present the formula for the effective reproduction number and give an estimate of it over the time. By conducting Latin Hyperbolic Sampling (LHS), evaluating the partial rank correlation coefficients (PRCCs) and other sensitivity analysis, we have found that increasing the transmission probability in contact with the mutant strain, the proportion of infecteds with mutant strain, the ratio of probability of the vaccinated individuals being infected, or the indirect transmission rate, all could aggravate the outbreak by raising the total number of deaths. We also found that increasing the recovery rate of those infecteds with mutant strain while decreasing their disease-induced death rate, or raising the vaccination rate, both could alleviate the outbreak by reducing the deaths. Our results demonstrate that reducing the prevalence of the mutant strain, improving the clearance of the virus in the environment, and strengthening the ability to treat infected individuals are critical to mitigate and control the spread of COVID-19, especially in the resource-constrained regions.

Global investigation for an "SIS" model for COVID-19 epidemic with asymptomatic infection

In this paper, we analyse a dynamical system taking into account the asymptomatic infection and we consider optimal control strategies based on a regular network. We obtain basic mathematical results for the model without control. We compute the basic reproduction number (R) by using the method of the next generation matrix then we analyse the local stability and global stability of the equilibria (disease-free equilibrium (DFE) and endemic equilibrium (EE)). We prove that DFE is LAS (locally asymptotically stable) when R<1 and it is unstable when R>1. Further, the existence, the uniqueness and the stability of EE is carried out. We deduce that when R>1, EE exists and is unique and it is LAS. By using generalized Bendixson-Dulac theorem, we prove that DFE is GAS (globally asymptotically stable) if R<1 and that the unique endemic equilibrium is globally asymptotically stable when R>1. Later, by using Pontryagin's maximum principle, we propose several reasonable optimal control strategies to the control and the prevention of the disease. We mathematically formulate these strategies. The unique optimal solution was expressed using adjoint variables. A particular numerical scheme was applied to solve the control problem. Finally, several numerical simulations that validate the obtained results were presented.

Mathematical analysis of a COVID-19 model with different types of quarantine and isolation

A COVID-19 deterministic compartmental mathematical model with different types of quarantine and isolation is proposed to investigate their role in the disease transmission dynamics. The quarantine compartment is subdivided into short and long quarantine classes, and the isolation compartment is subdivided into tested and non-tested home-isolated individuals and institutionally isolated individuals. The proposed model has been fully analyzed. The analysis includes the positivity and boundedness of solutions, calculation of the control reproduction number and its relation to all transmission routes, existence and stability analysis of disease-free and endemic equilibrium points and bifurcation analysis. The model parameters have been estimated using a dataset for Oman. Using the fitted parameters, the estimated values of the control reproduction number and the contribution of all transmission routes to the reproduction number have been calculated. Sensitivity analysis of the control reproduction number to model parameters has also been performed. Finally, numerical simulations to demonstrate the effect of some model parameters related to the different types of quarantine and isolation on the disease transmission dynamics have been carried out, and the results have been demonstrated graphically.

Modelling and stability analysis of ASFV with swill and the virus in the environment

African swine fever (ASF) is an acute, hemorrhagic and severe infectious disease caused by the African swine fever virus (ASFV), and leads to a serious threat to the pig industry in China. Yet the impact of the virus in the environment and contaminated swill on the ASFV transmission is unclear in China. Then we build the ASFV transmission model with the virus in the environment and swill. We compute the basic reproduction number, and prove that the disease-free equilibrium is globally asymptotically stable when $ R_0 < 1 $ and the unique endemic equilibrium is globally asymptotically stable when $ R_0 > 1 $. Using the public information, parameter values are evaluated. PRCCs and eFAST sensitivity analysis reveal that the release rate of ASFV from asymptomatic and symptomatic infectious pigs and the proportion of pig products from infectious pigs to swill have a significant impact on the ASFV transmission. Our findings suggest that the virus in the environment and contaminated swill contribute to the ASFV transmission. Our results may help animal health to prevent and control the ASFV transmission.

Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of <0.1%, <1%, and <10%, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions.

Stability analysis and optimal control of COVID-19 with quarantine and media awareness

In this paper, an improved COVID-19 model is given to investigate the influence of treatment and media awareness, and a non-linear saturated treatment function is introduced in the model to lay stress on the limited medical conditions. Equilibrium points and their stability are explored. Basic reproduction number is calculated, and the global stability of the equilibrium point is studied under the given conditions. An object function is introduced to explore the optimal control strategy concerning treatment and media awareness. The existence, characterization and uniqueness of optimal solution are studied. Several numerical simulations are given to verify the analysis results. Finally, discussion on treatment and media awareness is given for prevention and treatment of COVID-19.

Prediction of slope stability using Tree Augmented Naive-Bayes classifier: modeling and performance evaluation

Predicting slope stability is critical for identifying terrain that is prone to landslides and mitigating the damage caused by landslides. The relationships between factors that determine slope instability are complicated and multi-factorial, so it is sometimes difficult to mathematically characterize slope stability. In this paper, new Tree Augmented Naive-Bayes (TAN) model was developed to predict slope stability subjected to circular failures based on six input factors: cohesion, internal friction angle, pore pressure ratio, slope angle, unit weight, and slope angle. A total 87 slope stability case records obtained from published literature was used to train and test the proposed TAN model. According to the results of the performance indices-accuracy, precision, recall, F-score and Matthews correlation coefficient, the established TAN model was proven to be better at predicting slope stability with acceptable accuracy than other formerly developed empirical models in the literature. Furthermore, the slope height was revealed as the most sensitive factor in a sensitivity analysis.

Discrete epidemic modelling of COVID-19 transmission in Shaanxi Province with media reporting and imported cases

The large-scale infection of COVID-19 has led to a significant impact on lives and economies around the world and has had considerable impact on global public health. Social distancing, mask wearing and contact tracing have contributed to containing or at least mitigating the outbreak, but how public awareness influences the effectiveness and efficiency of such approaches remains unclear. In this study, we developed a discrete compartment dynamic model to mimic and explore how media reporting and the strengthening containment strategies can help curb the spread of COVID-19 using Shaanxi Province, China, as a case study. The targeted model is parameterized based on multi-source data, including the cumulative number of confirmed cases, recovered individuals, the daily number of media-reporting items and the imported cases from the rest of China outside Shaanxi from January 23 to April 11, 2020. We carried out a sensitivity analysis to investigate the effect of media reporting and imported cases on transmission. The results revealed that reducing the intensity of media reporting, which would result in a significant increasing of the contact rate and a sizable decreasing of the contact-tracing rate, could aggravate the outbreak severity by increasing the cumulative number of confirmed cases. It also demonstrated that diminishing the imported cases could alleviate the outbreak severity by reducing the length of the epidemic and the final size of the confirmed cases; conversely, delaying implementation of lockdown strategies could prolong the length of the epidemic and magnify the final size. These findings suggest that strengthening media coverage and timely implementing of lockdown measures can significantly reduce infection.

Probabilistic evaluation of CPT-based seismic soil liquefaction potential: towards the integration of interpretive structural modeling and bayesian belief network

This paper proposes a probabilistic graphical model that integrates interpretive structural modeling (ISM) and Bayesian belief network (BBN) approaches to predict cone penetration test (CPT)-based soil liquefaction potential. In this study, an ISM approach was employed to identify relationships between influence factors, whereas BBN approach was used to describe the quantitative strength of their relationships using conditional and marginal probabilities. The proposed model combines major causes, such as soil, seismic and site conditions, of seismic soil liquefaction at once. To demonstrate the application of the propose framework, the paper elaborates on each phase of the BBN framework, which is then validated with historical empirical data. In context of the rate of successful prediction of liquefaction and non-liquefaction events, the proposed probabilistic graphical model is proven to be more effective, compared to logistic regression, support vector machine, random forest and naive Bayes methods. This research also interprets sensitivity analysis and the most probable explanation of seismic soil liquefaction appertaining to engineering perspective.

Dynamical analysis of the spread of African swine fever with the live pig price in China

Pork makes up the highest proportion of household expenditure on meat in China and supply and demand have been basically stable in the past decade. However, the catastrophic outbreak of African swine fever (ASF) in August 2018 disrupted the balance and reduced the national herd by half within six months. The consequence was a gross lack of supply to the market and consumer demand was unable to be met. Accordingly, live pig prices rose sharply from 2019. In order to assess the influence of ASF on the price of the live pigs, we use a price function to characterize the relationship between price of the live pigs and the nation's pig stock, and then establish a time delay ASF epidemic dynamical model with the price function. By analyzing the dynamical behaviors of the model, we calculate the basic reproductive number, discuss the stability of equilibrium, and obtain the critical conditions for Hopf bifurcation. The model reasonableness is confirmed by carrying out data fitting and parameter estimation based on price data of the live pigs, the pig stock data and the outbreak data of ASF. By performing sensitivity analysis, we intuitively show the impact of ASF on the price of live pigs and the pig stocks, and assess the key factors affecting the outbreak of ASF. The conclusion is drawn that, with the control measures adopted by related government department in China, the basic reproductive number ($ R_0 = 0.6005 $) means that the ASF epidemic has been controlled. Moreover, the price of the live pig increases linearly with $ R_0 $, while the effect of the number of infected pigs on the subsequent price is non-linear related. Our findings suggest that society and the government should pay more attention to the prevention of animal disease epidemics.

Characterisation of transient electromagnetic signals during fixed interference sources in tunnel structure

The detection effect of the transient electromagnetic method is ambiguous in engineering applications due to the existence of interference sources, so explaining the influence of these fixed interference sources on is crucial. In this paper, the response characterisation of transient electromagnetic signals of fixed interference sources are thoroughly investigated. First, the secondary field generated by these interference sources is analyzed, and a typical fixed interference source is calculated. Then, a sensitivity analysis of the transient electromagnetic response curve is carried out. Finally, the mathematical superposition method for multiple field sources is proposed and verified. The results illustrate that the transient electromagnetic response curve of uniform full-space surrounding rock with a single fixed interference source has an apparent lifting phenomenon in the middle stage and presents an approximate horizontal change rule at the late stage. The transient electromagnetic response curves of multiple field sources separately illustrate the response characterisation of different field sources at different time stages. These research results can provide a valuable reference for the on-site interpretation of detection signals.

A mathematical model for the dynamics of SARS-CoV-2 virus using the Caputo-Fabrizio operator

The pandemic of SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics which spread worldwide through human interactions. The current study is focusing on the investigation and analysis of a fractional-order epidemic model that discusses the temporal dynamics of the SARS-CoV-2 virus in a community. It is well known that symptomatic and asymptomatic individuals have a major effect on the dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups of the population. Further, we assume that the vaccine confers permanent immunity because multiple vaccinations have commenced across the globe. The new fractional-order model for the transmission dynamics of SARS-CoV-2 virus is formulated via the Caputo-Fabrizio fractional-order approach with the maintenance of dimension during the process of fractionalization. The theory of fixed point will be used to show that the proposed model possesses a unique solution whereas the well-posedness (bounded-ness and positivity) of the fractional-order model solutions are discussed. The steady states of the model are analyzed and the sensitivity analysis of the basic reproductive number is explored. Moreover to parameterize the model a real data of SARS-CoV-2 virus reported in the Sultanate of Oman from January 1st, 2021 to May 23rd, 2021 are used. We then perform the large scale numerical findings to show the validity of the analytical work.

A simple model of cardiac mitochondrial respiration with experimental validation

Cardiac mitochondria are intracellular organelles that play an important role in energy metabolism and cellular calcium regulation. In particular, they influence the excitation-contraction cycle of the heart cell. A large number of mathematical models have been proposed to better understand the mitochondrial dynamics, but they generally show a high level of complexity, and their parameters are very hard to fit to experimental data. We derived a model based on historical free energy-transduction principles, and results from the literature. We proposed simple expressions that allow to reduce the number of parameters to a minimum with respect to the mitochondrial behavior of interest for us. The resulting model has thirty-two parameters, which are reduced to twenty-three after a global sensitivity analysis of its expressions based on Sobol indices. We calibrated our model to experimental data that consists of measurements of mitochondrial respiration rates controlled by external ADP additions. A sensitivity analysis of the respiration rates showed that only seven parameters can be identified using these observations. We calibrated them using a genetic algorithm, with five experimental data sets. At last, we used the calibration results to verify the ability of the model to accurately predict the values of a sixth dataset. Results show that our model is able to reproduce both respiration rates of mitochondria and transitions between those states, with very low variability of the parameters between each experiment. The same methodology may apply to recover all the parameters of the model, if corresponding experimental data were available.

Reproduction number and sensitivity analysis of cassava mosaic disease spread for policy design

We develop a mathematical model for the dynamics of Cassava Mosaic Disease (CMD), which is driven by both planting of infected cuttings and whitefly transmission. We use the model to analyze the dynamics of a CMD outbreak and to identify the most cost-effective policy for controlling it. The model uses the reproduction number $ \mathscr{R}_0 $ as a threshold, calculated using the Next-Generation Method. A locally-asymptotically-stable disease-free equilibrium is established when $ \mathscr{R}_0 < 1 $, proved by the Routh-Hurwitz criterion. The globally-asymptotically-stable disease-free and endemic-equilibrium points are obtained using Lyapunov's method and LaSalle's invariance principle. Our results indicate that the disease-free equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 \leq 1 $, while the endemic-equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 > 1 $. Our sensitivity analysis shows that $ \mathscr{R}_0 $ is most sensitive to the density of whitefly. Numerical simulations confirmed the effectiveness of whitefly control for limiting an outbreak while minimizing costs.

Transmission dynamics and optimal control of a Huanglongbing model with time delay

In this paper, a mathematical model has been formulated for the transmission dynamics of citrus Huanglongbing considering latent period as the time delay factor. Existence of the equilibria and their stability have been studied on the basis of basic reproduction number in two cases τ=0 and τ>0. The results show that stability changes occur through Hopf bifurcation in the delayed system. Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using three time-dependent control variables determined from sensitivity analysis. By using Pontryagin's Maximum Principle, we obtain the optimal integrated strategy and prove the uniqueness of optimal control solution. Analytical and numerical findings suggest that it is feasible to implement control techniques while minimizing the cost of implementation of optimal control strategies.

Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator

We propose an uncertainty propagation study and a sensitivity analysis with the Ocular Mathematical Virtual Simulator, a computational and mathematical model that predicts the hemodynamics and biomechanics within the human eye. In this contribution, we focus on the effect of intraocular pressure, retrolaminar tissue pressure and systemic blood pressure on the ocular posterior tissue vasculature. The combination of a physically-based model with experiments-based stochastic input allows us to gain a better understanding of the physiological system, accounting both for the driving mechanisms and the data variability.

A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic

In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role.

Mathematical analysis of a human papillomavirus transmission model with vaccination and screening

We formulate a mathematical model to explore the transmission dynamics of human papillomavirus (HPV). In our model, infected individuals can recover with a limited immunity that results in a lower probability of being infected again. In practice, it is necessary to revaccinate individuals within a period after the first vaccination to ensure immunity to HPV infection. Accordingly, we include vaccination and revaccination in our model. The model exhibits backward bifurcation as a result of imperfect protection after recovery and because the basic reproduction number is less than one. We conduct sensitivity analysis to identify the factors that markedly affect HPV infection rates and propose an optimal control problem that minimizes vaccination and screening cost. The optimal controls are characterized according to Pontryagin's maximum principle and numerically solved by the symplectic pseudospectral method.

A new model of dengue fever in terms of fractional derivative

It is eminent that the epidemiological patterns of dengue are threatening for both the global economy and human health. The experts in the field are always in search to have better mathematician models in order to understand the transmission dynamics of epidemics models and to suggest possible control or the minimization of the infection from the community. In this research, we construct a new fractional-order system for dengue infection with carrier and partially immune classes to visualize the intricate dynamics of dengue. By using the basics of fractional theory, we determine the fundamental results of the proposed fractional-order dengue model. We obtain the basic reproduction number $R_0$ by next generation method and present the results based on it. The stability results are established for the infection-free state of the system. Moreover, sensitivity of $R_0$ is analyzed through partial rank correlation coefficient(PRCC) method to show the importance of different parameters in $R_0$. The influence of different input factors is shown on the output of basic reproduction number $R_0$ numerically. Our result showed that the threshold parameter $R_0$ can be decreased by increasing vaccination and treatment in the system. Finally, we illustrate the solution of the suggested dengue system through a numerical scheme to notice the influence of the fractional-order $\vartheta$ on the system. We observed that the fractional-order dynamics can explain the complex system of dengue infection more precisely and accurately rather than the integer-order dynamics. In addition, we noticed that the index of memory and biting rate of vector can play a significant part in the prevention of the infection.

Investigation of a measles transmission with vaccination: a case study in Jakarta, Indonesia

Measles is a contagious disease caused by the measles virus of genus Morbillivirus, which has been spreading in many affected regions. This infection is characterized by the appearance of rashes all over the body and potentially cause serious complications, especially among infants and children. Before measles immunization was promoted, it is one of the endemic diseases that caused the most fatalities each year in the world. This paper aims to analyze and to investigate measles transmission in Jakarta via an SIHR epidemic model involving vaccination from January to December 2017. Jakarta Health Office collected the observed data of measles incidence. We then derived the basic reproduction number as a threshold of disease transmission and obtained the local as well as global stability of the equilibria under certain conditions. The unobserved parameters and initial conditions were estimated by minimizing errors between data and numerical results. Furthermore, a stochastic model was developed to capture the data and to accommodate the randomness of the transmission. Sensitivity analysis was also performed to analyze and to identify the parameters which give significant contributions to the spread of the virus. We then obtained simulations of vaccine level coverage. The data is shown within a 95% confidence interval of the stochastic solutions, and the average of the stochastic solutions is relatively close to the solution of the deterministic model. The most sensitive parameter in the infected compartment is the hospitalized rate, which can be considered to be one of the essential factors to reduce the number of cases for policymakers. We hence proposed a control strategy which is providing treatment accesses easier for infected individuals is better than vaccinating when an outbreak occurs.

Effects of media reporting on mitigating spread of COVID-19 in the early phase of the outbreak

The 2019 novel coronavirus disease (COVID-19) is running rampantly in China and is swiftly spreading to other countries in the world, which causes a great concern on the global public health. The absence of specific therapeutic treatment or effective vaccine against COVID-19 call for other avenues of the prevention and control measures. Media reporting is thought to be effective to curb the spreading of an emergency disease in the early stage. Cross-correlation analysis based on our collected data demonstrated a strong correlation between media data and the infection case data. Thus we proposed a deterministic dynamical model to examine the interaction of the disease progression and the media reports and to investigate the effectiveness of media reporting on mitigating the spread of COVID-19. The basic reproduction number was estimated as 5.3167 through parameterization of the model with the number of cumulative confirmed cases, the number of cumulative deaths and the daily number of media items. Sensitivity analysis suggested that, during the early phase of the COVID-19 outbreak, enhancing the response rate of the media reporting to the severity of COVID-19, and enhancing the response rate of the public awareness to the media reports, both can bring forward the peak time and reduce the peak size of the infection significantly. These findings suggested that besides improving the medical levels, media coverage can be considered as an effective way to mitigate the disease spreading during the initial stage of an outbreak.

Modeling Citrus Huanglongbing transmission within an orchard and its optimal control

Citrus Huanglongbing (HLB) is the most devastating citrus disease worldwide. In this paper, a deterministic dynamical model is proposed to explore the transmission dynamics of HLB between citrus tree and Asian citrus psyllid (ACP). Using the theory of dynamical system, the dynamics of the model are rigorously analyzed. The results show that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number $\mathscr{R}_0 < 1$, and when $\mathscr{R}_0 > 1$ the system is uniformly persistent. Applying the global sensitivity analysis of $\mathscr{R}_0$, some parameters that have the greatest impact on HLB transmission dynamics are obtained. Furthermore, the optimal control theory is applied to the model to study the corresponding optimal control problem. Both analytical and numerical results show that: (1) the infected ACP plays a decisive role in the transmission of HLB in citrus trees, and eliminating the ACP will be helpful to curtail the spread of HLB; (2) optimal control strategy is superior to the constant control strategy in decreasing the prevalence of the diseased citrus trees, and the cost of implementing optimal control is much lower than that of the constant control strategy; and (3) spraying insecticides is more effective than other control strategies in reducing the number of ACP in the early phase of the transmission of HLB. These theoretical and numerical results may be helpful in making public policies to control HLB in orchards more effectively.

Mathematical analysis and simulation of a Hepatitis B model with time delay: A case study for Xinjiang, China

The incubation period for Hepatitis B virus (HBV) within the human is epidemiologically significant because it is typically of long duration (1.5∼6 months) and the disease transmission possibility may be increased due to more contact from the patients in this period. In this paper, we investigate an SEICRV epidemic model with time delay to research the transmission dynamics of Hepatitis B disease. The basic reproductive number ${\mathcal R}_0$ is derived and can determine the dynamics of the model. The disease-free equilibrium is globally asymptotically stable if ${\mathcal R}_0<1 and="" unstable="" if="" mathcal="" r="" _0="">1$. As ${\mathcal R}_0>1$, the model admits a unique endemic equilibrium which is locally asymptotically stable. The endemic equilibrium is globally asymptotically stable when the vertical transmission is ignored. Numerically, we study the Hepatitis B transmission case in Xinjiang, China. Using the Hepatitis B data from Xinjiang, the basic reproductive number is estimated as 1.47 (95% CI: 1.34-1.50). By the end of 2028, the cumulative number of Hepatitis B cases in Xinjiang will be estimated about 700,000 if there is no more effective preventive measures. The sensitivity analysis of ${\mathcal R}_0$ in terms of parameters indicates prevention and treatment for chronic patients are key measures in controlling the spread of Hepatitis B in Xinjiang.

Mathematical models for within-host competition of malaria parasites

In this paper, we formulate two within-host infection models to simulate dynamics of the drug sensitive and drug resistant malaria parasites, where the first model solely considers the within-host competition between these two strains, and the second model further considers the immune re-sponse. Detailed theoretical analysis of the second model are made, including the existence, stability and bifurcation of the equilibrium, which have also been verified by numerical simulations. Both theoretical and numerical results show that competition or chronic control of drug sensitive parasites could inhibit the evolution of drug resistant ones to some extent. However, if the immune response is considered, periodic solution could be observed, and they will persist for all relatively small treatment rate. This may lead to the recurrence of resistance for the chronic control strategy, even though it could delay the resistance emergence. In addition, global sensitivity analysis is implemented to provide the information on the significance of model parameters on the state variables.

Using cultural, historical, and epidemiological data to inform, calibrate, and verify model structures in agent-based simulations

Agent-based simulation models are excellent tools for addressing questions about the spread of infectious diseases in human populations because realistic, complex behaviors as well as random factors can readily be incorporated. Agent-based models are flexible and allow for a wide variety of behaviors, time-related variables, and geographies, making the calibration process an extremely important step in model development. Such calibration procedures, including verification and validation, may be complicated, however, and usually require incorporation of substantial empirical data and theoretical knowledge of the populations and processes under study. This paper describes steps taken to build and calibrate an agent-based model of epidemic spread in an early 20^th century fishing village in Newfoundland and Labrador, including a description of some of the detailed ethnographic and historical data available. We illustrate how these data were used to develop the structure of specific parts of the model. The resulting model, however, is designed to reflect a generic small community during the early 20^th century and the spread of a directly transmitted disease within such a community, not the specific place that provided the data. Following the description of model development, we present the results of a replication study used to confirm the model behaves as intended. This study is also used to identify the number of simulations necessary for high confidence in average model output. We also present selected results from extensive sensitivity analyses to assess the effect that variation in parameter values has on model outcomes. After careful calibration and verification, the model can be used to address specific practical questions of interest. We provide an illustrative example of this process.

EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity

The paper is devoted to the analysis of electroencephalography (EEG) in neonates. The goal is to investigate the impact of fontanels on EEG measurements, i.e. on the values of the electric potential on the scalp. In order to answer this clinical issue, a complete mathematical study (modeling, existence and uniqueness result, realistic simulations) is carried out. A model for the forward problem in EEG source localization is proposed. The model is able to take into account the presence and ossification process of fontanels which are characterized by a variable conductivity. From a mathematical point of view, the model consists in solving an elliptic problem with a singular source term in an inhomogeneous medium. A subtraction approach is used to deal with the singularity in the source term, and existence and uniqueness results are proved for the continuous problem. Discretization is performed with 3D Finite Elements of type P1 and error estimates are proved in the energy norm (H¹-norm). Numerical simulations for a three-layer spherical model as well as for a realistic neonatal head model including or not the fontanels have been obtained and corroborate the theoretical results. A mathematical tool related to the concept of Gâteau derivatives is introduced which is able to measure the sensitivity of the electric potential with respect to small variations in the fontanel conductivity. This study attests that the presence of fontanels in neonates does have an impact on EEG measurements.