Frontiers in Applied Mathematics and Statistics

Hepatitis B is the main public health problem of the whole world. In epidemiology, mathematical models perform a key role in understanding the dynamics of infectious diseases. This paper proposes Pade approximation (Pa) with Differential Evolution (DE) for obtaining solution of Hepatitis-B model which is nonlinear numerically. The proposed strategy transforms the nonlinear model into optimization problem by using Pade approximation. Initial conditions are converted into problem constraints and constraint problem become unconstraint by using penalty function. DE is obtained numerical solution of Hepatitis-B model by solving the established problem of optimization. There is no need to choose step lengths in proposed Pade-approximation based Differential Evolution (PaDE) technique and also PaDE converges to true steady state points. Finally, a convergence and error analysis evidence that the convergence speed of PaDE is greater than Non-Standard Finite Difference (NSFD) method for different time steps.

Pneumonia has been a major airborne transmitted disease and continues to pose a major public health burden in both developed and developing countries of the world. In this study, we constructed and analyzed a nonlinear deterministic compartmental mathematical model for assessing the community-level impacts of vaccination, other protection measures like practicing good hygiene, avoiding close contacts with sick people and limiting exposure to cigarette smoke, etc. and treatment on the transmission dynamics of pneumonia disease in a population of varying size. Our model exhibits two kinds of equilibrium points: pneumonia disease-free equilibrium point, and pneumonia endemic equilibrium point(s). Using center manifold criteria, we have verified that the pneumonia model exhibits backward bifurcations whenever its effective reproduction number [R]P < 1 and in the same region, the model shows the existence of more than one endemic equilibrium point where some of which are stable and others are unstable. Thus, for pneumonia infection, the necessity of the pneumonia effective reproduction number [R]P < 1, although essential, it might not be enough to completely eradicate the pneumonia infection from the considered community. Our examination of sensitivity analysis shows that the pneumonia infection transmission rate denoted by {beta} plays a crucial role to change the qualitative dynamics of pneumonia infection. By taking standard data from published literature, our numerical computations show that the numerical value of pneumonia infection model effective reproduction number is [R]P = 8.31 at {beta} = 4.21 it implies that the disease spreads throughout the community. Finally, our numerical simulations show that protection, vaccination, and treatment against pneumonia disease have the effect of decreasing pneumonia expansion.

Growth is a dynamic activity of simultaneous biological processes happening at multiple time-scales varying from orders of fractions of a second to several years. Rather than modeling growth with differential equations, this multiple time-scale dynamics is modeled using a simpler algebraic approach that involves continued fraction of the linear time scale. This algebraic approach offers models that are infinitely differentiable like an exponential function but also robust and superposable like linear equations. Thus, unique insights into growth dynamics can be obtained without much need of a calculus background. Growth of bacterial colonies, yeast cultures, Drosophila population, mean individual attributes of Helianthus and rats have already been modeled using this approach. In this work, we extend the modeling procedure to individual human growth using Montbeillards height measurements of his son starting from birth upto almost 18 years of age. Good fits are obtained on the data and growth rates are estimated directly from the model. Thus, this methodology provides generic, flexible, simpler and more interpretable growth models.

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.

It is well-known that the Tseng algorithm and its modifications have been successfully employed in approximating zeros of the sum of monotone operators. In this study, we restored various thoracic diseases computerized tomography (CT) images, which were degraded with a known blur function and additive noise, using a modified Tseng algorithm. The test images used in the study depict calcification of the Aorta, Subcutaneous Emphysema, Tortuous Aorta, Pneumomediastinum, and Pneumoperitoneum. Additionally, we employed well-known image restoration tools to enhance image quality and compared the quality of restored images with the originals. Finally, the study demonstrates the potential to advance monotone inclusion problem-solving, particularly in the field of medical image recovery.

The paper assumed that Nf2-Amot complex regulates the phosphorylation cascade so that each cell in the early mammalian embryo differentiates properly in silico. To confirm the validity of the assumption, it was necessary to verify whether Nf2-Amot complex has an impact on the resulting differentiation. The living embryo is unsuitable for the confirmation since the early mammalian embryo is too small to observe and too ethically sensitive to invade. In such cases, computational models can be used as experimental subjects for operations that cannot be applied to the living embryo. Previous models on the embryo, however, could not verify the assumption because they had not modeled Nf2-Amot complex, and they seldom modeled the Hippo signaling pathway. Therefore, the paper introduced a model of Nf2-Amot complex to the previous study that had modeled the Hippo signaling pathway. Testing the model under diverse conditions revealed that the existence of Nf2-Amot complex reproduces the ideal cell differentiation observed in the living embryo. In this sense, the validity of the model was confirmed. Furthermore, diverse cell-cell contacts that induce various concentrations of Nf2-Amot complex also resulted in ideal cell differentiation. These results suggested the correctness of the assumption in silico.

Estimation of COVID-19 dynamics and its evolution is a multidisciplinary effort, which requires the unification of heterogeneous disciplines (scientific, mathematics, epidemiological, biological/bio-chemical, virologists and health disciplines to mention the most relevant) to work together in a better understanding of this pandemic. Time series analysis is of great importance to determine both the similarity in the behavior of COVID-19 in certain countries/states and the establishment of models that can analyze and predict the transmission process of this infectious disease. In this contribution, an analysis of the different states of the United States will be carried out to measure the similarity of COVID-19 time series, using dynamic time warping distance (DTW) as a distance metric. A parametric methodology is proposed to jointly analyze infected and deceased persons. This metric allows to compare time series that have a different time length, making it very appropriate for studying the United States, since the virus did not spread simultaneously in all the states/provinces. After a measure of the similarity between the time series of the states of United States was determined, a hierarchical cluster was created, which makes it possible to analyze the behavioral relationships of the pandemic between different states and to discover interesting patterns and correlations in the underlying data of COVID-19 in the United States. With the proposed methodology, nine different clusters were obtained, showing a different behavior in the eastern zone and western zone of the United States. Finally, to make a prediction of the evolution of COVID-19 in the states, Logistic, Gompertz and SIR model was computed. With these mathematical model it is possible to have a more precise knowledge of the evolution and forecast of the pandemic.

Following the suggestion of L. F. Jaffe [1] we propose a mathematical model of fast calcium induced calcium influx waves (CICI Waves). They can propagate at relatively high speeds (up to 1300 micrometers/s). According to [1], they propagate due to a mechanochemical interaction of actomyosin network with the cell membrane. The local stretching of the membrane caused by actin filaments opens mechanically operated ion channels resulting in the influx of calcium to the cell. Moreover, stretching a cells membrane at one point opens nearby stretch activated calcium channels because the mechanical force is relayed by the actin filaments interconnected by myosin bridges. The number of bridges as well as filament density increases with calcium concentration, causing the contraction of the actomyosin network. Thus, the force acting on the membrane from tangled actin filaments is transmitted ahead of the moving front of the calcium concentration. As a result, the ion channels are opened even before the signal of calcium reaches them. This leads to much larger propagation speed of CICI waves in comparison with calcium induced calcium released (CICR) waves, where the wave is sustained by the diffusion of calcium and autocatalytic release of calcium from the internal stores (e.g. endoplasmic reticula).

Current research is an attempt to understand the CoVID-19 pandemic curve through statistical approach of probability density function with associated skewness and kurtosis measures, change point detection and polynomial fitting to estimate infected population along with 30 days projection. The pandemic curve has been explored for above average affected countries, six regions and global scale during 64 days of 22nd January to 24th March, 2020. The global cases infection as well as recovery rate curves remained in the ranged of 0 - 9.89 and 0 - 8.89%, respectively. The confirmed cases probability density curve is high positive skewed and leptokurtic with mean global infected daily population of 6620. The recovered cases showed bimodal positive skewed curve of leptokurtic type with daily recovery of 1708. The change point detection helped to understand the CoVID-19 curve in term of sudden change in term of mean or mean with variance. This pointed out disease curve is consist of three phases and last segment that varies in term of day lengths. The mean with variance based change detection is better in differentiating phases and associated segment length as compared to mean. Global infected population might rise in the range of 0.750 to 4.680 million by 24th April 2020, depending upon the pandemic curve progress beyond 24th March, 2020. Expected most affected countries will be USA, Italy, China, Spain, Germany, France, Switzerland, Iran and UK with at least infected population of over 0.100 million. Infected population polynomial projection errors remained in the range of -78.8 to 49.0%.

This paper introduces an optimal control strategy for choleras crossover mathematical model. The proposed model integrates {Psi}-Caputo fractal variable-order derivatives, fractal fractional-order derivatives, and integer-order derivatives across three distinct time intervals, utilizing a simple non-standard kernel function {Psi}(t). A comprehensive stability analysis of the models steady states is conducted. The models results are compared with real-world data from the cholera outbreak in Yemen. Following this, an optimal control problem is formulated within the crossover framework. To numerically solve the resulting optimality system, a discretized non-standard -finite difference method is developed. Numerical simulations and comparative studies are presented to demonstrate the methods applicability and the efficiency of the approximation approach. The key finding of this study highlights that the crossover-controlled system proves to be the most effective approach for mitigating and controlling the spread of cholera.

The novel coronal virus has spread across more than 213 countries within the space of six months causing devastating public health hazard and monumental economic loss. In the absence of clinically approved pharmaceutical intervention, attentions are shifted to non-pharmaceutical controls to mitigate the burden of the novel pandemic. In this regard, a ten mutually exclusive compartmental mathematical model is developed to investigate possible effects of both pharmaceutical and non-pharmaceutical controls incorporating both private and governments quarantine and treatments. Several reproduction numbers were calculated and used to determine the impact of both control measures as well as projected benefits of social distancing, treatments and vaccination. We investigate and compare the possible impact of social distancing incorporating different levels of vaccination, with vaccination programme incorporating different levels of treatment. Using the officially published South African COVID-19 data, the numerical simulation shows that the community reproduction threshold will be 30 when there is no social distancing but will drastically reduced to 5 (about 83% reduction) when social distancing is enforced. Furthermore, when there is vaccination with perfect efficacy, the community reproduction threshold will be 4 which increases to 12 (about 67% increment) with-out vaccination. We also established that the implementation of both interventions is enough to curtail the spread of COVID-19 pandemic in South Africa which is in confirmation with the recommendation of the world health organization.

In this article, we are going to study the current COVID-19 spread patterns in India and the United States. We are interested to show how the daily increase in the total number of cases in these two countries is affecting the COVID-19 spread pattern in the World. For the study, we have considered the cumulative total numbers of cases in India, the United States and the World. We have found that the situation in the United States is already on the threshold of a change towards retardation. In the World as a whole also we have observed that a similar conclusion can be made. In India, the situation can be expected to move towards betterment soon, and once that happens the situation in the World as a whole would start improving. We shall demonstrate that as long as the rate of change of the logarithm of the cumulative total number of cases with respect to time in a pandemic continues to reduce, the pattern of growth would continue to remain nearly exponential, and as soon as it is seen that the rate of change starts to become nearly constant the growth can be expected to start to change towards a nearly logarithmic pattern.

We study in this work some statistical methods to estimate the parameters resulting from the use of an age-structured contact mathematical epidemic model in order to analyze the evolution of the epidemic curve of Covid-19 in the French overseas department Mayotte from march 13, 2020 to february 26,2021. Using several statistic methods based on time dependent method, maximum likelihood, mixture method, we fit the probability distribution which underlines the serial interval distribution and we give an adapted version of the generation time distribution from Package R0. The best-fit model of the serial interval was given by a mixture of Weibull distribution. Furthermore this estimation allows to obtain the evolution of the time varying effective reproduction number and hence the temporal transmission rates. Finally based on others known estimates parameters we incorporate the estimated parameters in the model in order to give an approximation of the epidemic curve in Mayotte under the conditions of the model. We also discuss the limit of our study and the conclusion concerned a probable impact of non pharmacological interventions of the Covid-19 in Mayotte such us the re-infection cases and the introduction of the variants which probably affect the estimates.

In Russia, COVID-19 has currently been growing hyper-exponentially. This type of a spread pattern was not seen during the first wave of the pandemic the world over. Indeed when the disease had first appeared, in the accelerating stage the spread pattern was observed to have followed a highly nonlinear pattern that could be said to be approximately exponential or sub-exponential. As to why in the resurgence the growth has become hyper-exponential is another matter. But this has been happening in Europe and how long this would continue cannot be predicted. It may so happen that in the countries in which retardation has already been taking place, there may be resurgence of the disease. It was observed that in the World as a whole, retardation was on the threshold during the second half of September. But if the resurgence happens to follow the hyper-exponential growth pattern in different countries, there may be resurgence in the World as a whole.

In two previous papers we have proposed models to estimate the Covid-19 epidemic when the number of daily positive cases has a bell shaped form that we call a mode. We have observed that each Covid variant produces this type of epidemic shape at a different moment, resulting in a multimodal epidemic shape. We will show in this document that each mode can still be estimated with models described in the two previous papers provides we replace the cumulated number of positive cases y by the cumulated number of positive cases reduced by a parameter P to be estimated. Therefore denoting z the logarithm of y -P, z follows approximately the differential equation [z] = b -azr where a, b, r have also to be estimated from the observed data. We will show the obtained predictions on the four French modes April, November 2020, May and September 2021. The comparison between the prediction obtained before the containment decisions made by the French government and the observed data afterwards suggests the inefficiency of the epidemic lockdowns.

Owing to the SARS-CoV-2 epidemic (severe acute respiratory coronavirus 2 syndromes), the global situation has changed drastically. Several countries, including India, Europe, U.S.A., introduced a full state/nation lockdown to minimize the disease transmission through human interaction after the virus entered the population and to minimize the loss of human life. Millions of people have gone unemployed due to lockdown implementation, resulting in business and industry closure and leading to a national economic slowdown. Therefore, preventing the spread of the COVID-19 virus in the world while also preserving the global economy is an essential problem requiring an effective and immediate solution. Using the compartmental epidemiology S, E, I, R or D (Susceptible, Exposed, Infectious, Recovery or Death) model extended to multiple population regions we predict the evolution of the SARS-CoV-2 disease and construct an optimally scheduled lockdown calendar to execute lockdown over phases, using the well-known Knapsack problem. A comparative analysis of both classical and quantum models shows that our model decreases SARS-CoV-2 active cases while retaining the average global economic factor, GDP, in contrast to the scenario with no lockdown.

A logistic formulation in biology is applied to analyze deaths by the third wave of COVID-19 in Japan.

In the present work, we propose a new integrated mathematical model for the neuromuscular activation of a motor unit, describing the four consecutive processes, leading to muscle contraction--neural impulse propagation, acetylcholine transport in the neuromuscular junction, calcium release in the muscle cell, and force generation. We connect in an appropriate way models of the respective processes, known from the literature, and validate the resulting model by showing that it can reproduce with high accuracy experimental data for two motor unit twitches on a rat medial gastrocnemius muscle and can numerically restore the sequence of events that result in force generation. Sensitivity analysis for some of the model parameters is further performed to study their effect on the model solutions and to show that they can be related to known malfunctions or treatments of the neuromuscular system.

Withdrawal StatementThe authors have withdrawn their manuscript owing to errors in the experimental design that affect the integrity of the results. Therefore, the authors do not wish this work to be cited as reference for the project. If you have any questions, please contact the corresponding author

Modelling the dynamics of mosquito borne disease (MBD) cases is a challenging task. The current study first proposes a generic dynamical model to qualitatively understand the seasonality as well as outbreaks of malaria and dengue over the state of Kerala based on a climate forced oscillator model, which is then supplemented by a data driven model for quantitative evaluation. The proposed forced oscillator model is parametric and general in nature which can be qualitatively used to understand the seasonality and outbreaks. However, since parametric model-based estimation require estimation of multiple parameters and several closure assumptions, we used the K-means clustering which is a data driven clustering approach to understand the relationship between Malaria and Dengue cases and climate forcing. The results showed a clear relationship of the MBD cases with the first order and second order moments (i.e. mean and standard deviation) of the climate forcing parameters. Based on this, we came up with an objective threshold criterion which relates the climate parameters to the number of cases of malaria and dengue cases over Kerala.