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Lung cancer is the biggest cause of cancer mortality worldwide and a major impediment to extending life expectancy. In comparison to other cancers, it has a relatively poor survival rate. In this paper, we have developed a mathematical model for lung cancer based on biological phenomena using nonlinear ordinary differential equations and analyzed it both analytically and numerically. According to the findings, CD8+ T cells and dendritic cells have a role in tumor cell variety. Surgery and chemotherapy have been used as treatment options, and we have observed that three doses of chemotherapy after surgery had the greatest results after examining several treatment options. During the treatment period, the cycle of each chemotherapy has been taken every 4 weeks, and the first dose has been taken after 28 days of surgery. Finally, we have evaluated the various starting dates for the best treatment choice and discovered that the patient who begins treatment sooner has a better probability of surviving. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) and coronavirus (COVID-19) are both infectious diseases that globally continue affecting millions of people every year. They have similar symptoms such as cough, fever, and difficulty breathing but differ in incubation periods. This paper introduces a mathematical model for the transmission dynamics of TB and COVID-19 coinfection using a system of nonlinear ordinary differential equations. The well-posedness of the proposed coinfection model is then analytically studied by showing properties such as the existence, boundedness, and positivity of the solutions. The stability analysis of the equilibrium points of submodels is also discussed separately after computing the basic reproduction numbers. In each case, the disease-free equilibrium points of the submodels are proved to be both locally and globally stable if the reproduction numbers are less than unity. Besides, the coinfection disease-free equilibrium point is proved to be conditionally stable. The sensitivity and bifurcation analysis are also studied. Different simulation cases were performed to supplement the analytical results. [ABSTRACT FROM AUTHOR]

Generally speaking, spoken term detection system will degrade significantly because of mismatch between acoustic model and spontaneous speech. This paper presents an improved spoken term detection strategy, which integrated with a novel phoneme confusion matrix and an improved word-level minimum classification error (MCE) training method. The first technique is presented to improve spoken term detection rate while the second one is adopted to reject false accepts. On mandarin conversational telephone speech (CTS), the proposed methods reduce the equal error rate (EER) by 8.4% in relative. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlinear differential equation, by using the fixed point theory. The existence of the periodic solution of the nonlinear differential equation is obtained; these results are new. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R 0 , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R 0 > 1. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R 0 < 1 , and the unique endemic equilibrium point is locally asymptotically stable whenever R 0 > 1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R 0 = 1 , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R 0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis. [ABSTRACT FROM AUTHOR]

The first step in the analysis of a structure is to generate its configuration. Different means are available for this purpose. The use of graph products is an example of such tools. In this paper, the use of product graphs is extended for the formation of different types of structural models. Here weighted graphs are used as the generators and the connectivity properties of different models are expressed in terms of the properties of their generators through simple algebraic relationships. In this paper by using graph product concepts and spatial structured matrices, a new algebraic closed form is proposed for mathematical formulation and presentation of structures. For clarification some examples are included. [ABSTRACT FROM AUTHOR]

The study of precise large deviations of random sums is an important topic in insurance and finance. In this paper, extended precise large deviations of random sums in the presence of END structure and consistent variation are investigated. The obtained results extend those of Chen and Zhang (2007) and Chen et al. (2011). As an application, precise large deviations of the prospectiveloss process of a quasirenewal model are considered. [ABSTRACT FROM AUTHOR]

In this paper, we consider a cross-diffusion predator-prey model with sex structure. We prove that cross-diffusion can destabilize a uniform positive equilibrium which is stable for the ODE system and for the weakly coupled reaction-diffusion system. As a result, we find that stationary patterns arise solely from the effect of cross-diffusion. [ABSTRACT FROM AUTHOR]

It is with a great significance to discuss the selection model of regional strategic emerging industry. First, the paper uses the fuzzy optimization theory to select the central industry of area as the regional strategic emerging industry and try to optimize the weight's calculation in the multistage fuzzy comprehensive evaluation to get more accurate results. Then it will do a strategic emerging industrial inspection about the advantage and ecological related index based on a multiobjective programming model and the maximum entropy. [ABSTRACT FROM AUTHOR]

Nonclassical slicing and symmetry reduction can act as efficient structural abstract methods for pruning state space when dealing with verification problems. In this paper, we mainly address theoretical and algorithmic aspects for nonclassical slicing and symmetry reduction over prime event structures. We propose sliced and symmetric quotient reduction models of event structures and present their corresponding algorithms. To construct the underlying foundation of the proposed methodologies, we introduce strong and weak conflict concepts and a pair of mutually inverse operators and extend permutation group based symmetry notion of event structures. We have established a unified mathematical framework for slicing and symmetry reduction, and further investigated the translation, isomorphism, and equivalence relationship and other related basic facts from a theoretical point of view. The framework may provide useful guidance and theoretical exploration for overcoming verification challenges. This paper also demonstrates their practical applications by two cases. [ABSTRACT FROM AUTHOR]

In this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID-19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the model system including existence and uniqueness, positivity, and invariant region of solutions are proved under a certain meaningful set. The model exhibits two equilibrium points: disease-free and endemic equilibrium points under certain conditions. The basic reproduction number, R 0 , is derived via the next-generation matrix approach, and the dynamical behavior of the model is explored in detail. The analytical analysis reveals that the disease-free equilibrium solution is locally as well as globally asymptotically stable when the associated basic reproduction number is less than unity which indicates that COVID-19 dies out in the population. Also, the endemic equilibrium point is globally asymptotically stable whenever the associated basic reproduction number exceeds a unity which implies that COVID-19 establishes itself in the population. The sensitivity analysis of the basic reproduction number is computed to identify the most dominant parameters for the spreading out as well as control of infection and should be targeted by intervention strategies. Furthermore, we extended the considered model to optimal control problem system by introducing two time-dependent variables that represent the educational campaign to susceptibles and continuous treatment for quarantined individuals. Finally, some numerical results are illustrated to supplement the analytical results of the model using MATLAB ode45. [ABSTRACT FROM AUTHOR]

In recent times, all world banks have been threatened by the liquidity risk problem. This phenomenon represents a devastating financial threat to banks and may lead to irrecoverable consequences in case of negligence or underestimation. In this article, we study a mathematical model that describes the contagion of liquidity risk in the banking system based on the SIR epidemic model simulation. The model consists of three ordinary differential equations illustrating the interaction between banks susceptible or affected by liquidity risk and tending towards bankruptcy. We have demonstrated the bornness and positivity of the solutions, and we have mathematically analyzed this system to demonstrate how to control the banking system's stability. Numerical simulations have been illustrated by using real data to support the analytical results and prove the effects of different system parameters studied on the contagion of liquidity risk. [ABSTRACT FROM AUTHOR]

Modeling and testing for parallel software systems are very difficult, because the number of states and execution sequences expands significantly caused by parallel behaviors. In this paper, a model reduction method based on Coloured Petri Net (CPN) is shown, which could generate a functionality-equivalent and trace-equivalent model with smaller scale. Model-based testing for parallel software systems becomesmuch easier after the model is reduced by the reduction method. Specifically, a formal model for software system specification is constructed based on CPN. Then the places in the model are divided into input places, output places, and internal places; the transitions in the model are divided into input transitions, output transitions, and internal transitions. Internal places and internal transitions could be reduced if preconditions are matching, and some other operations should be done for functionality equivalence and trace equivalence. If the place and the transition are in a parallel structure, then many execution sequences will be removed from the state space. We have proved the equivalence and have analyzed the reduction effort, so that we could get the same testing result with much lower testing workload. Finally, some practices and a performance analysis show that the method is effective. [ABSTRACT FROM AUTHOR]

An improved Susceptible-Infected-Susceptible (SIS) epidemic diffusion model with population migration between two cities is modeled. Global stability conditions for both the disease-free equilibrium and the endemic equilibrium are analyzed and proved. The main contribution of this paper is reflected in epidemic modeling and analysis which considers unequal migration rates, and only susceptible individuals can migrate between the two cities. Numerical simulation shows when the epidemic diffusion system is stable, number of infected individuals in one city can reach zero, while the number of infected individuals in the other city is still positive. On the other hand, decreasing population migration in only one city seems not as effective as improving the recovery rate for controlling the epidemic diffusion. [ABSTRACT FROM AUTHOR]

Vehicle crash test is considered to be the most direct and common approach to assess the vehicle crashworthiness. However, it suffers from the drawbacks of high experiment cost and huge time consumption. Therefore, the establishment of a mathematical model of vehicle crash which can simplify the analysis process is significantly attractive. In this paper, we present the application of LPV-ARMAX model to simulate the car-to-pole collision with different initial impact velocities. The parameters of the LPVARMAX are assumed to have dependence on the initial impact velocities. Instead of establishing a set of LTI models for vehicle crashes with various impact velocities, the LPV-ARMAX model is comparatively simple and applicable to predict the responses of new collision situations different fromthe ones used for identification. Finally, the comparison between the predicted response and the real test data is conducted, which shows the high fidelity of the LPV-ARMAX model. [ABSTRACT FROM AUTHOR]

In this paper, we offer the generalization of the known technique of the construction of the gradient of the residual functional based on the statement of the conjugate problem for the case when the unknown function is complex valued. The notion of the reference frequency of the medium is introduced. Knowing the value of the reference frequency lets us judge the possibility of simultaneous definition of the dielectric permittivity and conductivity. [ABSTRACT FROM AUTHOR]

In this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number R 0 is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever R 0 < 1. Also, the endemic equilibrium point is locally and globally asymptotically stable whenever R 0 > 1. Then, the model was extended to optimal control, and some numerical simulations with and without optimal control are also performed to verify the theoretical analysis using MATLAB. Numerical simulation of optimal control model shows that the prevention and punishment strategy is the most effective strategy to reduce the dynamic transmission of corruption. [ABSTRACT FROM AUTHOR]

A mathematical model is proposed to study the dynamics of the transmission of rabies, incorporating predation of dogs by humans. The model is shown to have a unique disease-free equilibrium which is globally asymptotically stable whenever ℛ 0 ≤ 1. Local sensitivity analysis suggests that the disease can be controlled through reducing contact with infected dogs, increasing immunization of dogs, screening recruited dogs, culling of infected dogs, and use of dog meat as a delicacy. [ABSTRACT FROM AUTHOR]

Sub-Saharan Africa harbours the majority of the burden of Lassa fever. Clinical diseases, as well as high seroprevalence, have been documented in Nigeria, Sierra Leone, Liberia, Guinea, Ivory Coast, Ghana, Senegal, Upper Volta, Gambia, and Mali. Deaths from Lassa fever occur all year round but naturally peak during the dry season. Annually, the number of people infected is estimated at 100,000 to 300,000, with approximately 5,000 deaths. There have been some work done on the dynamics of Lassa fever disease transmission, but to the best of our knowledge, none has been able to capture the seasonal variation of Mastomys rodent population and its impact on the transmission dynamics. In this work, a periodically forced seasonal nonautonomous system of a nonlinear ordinary differential equation is developed that captures the dynamics of Lassa fever transmission and seasonal variation in the birth of Mastomys rodents where time was measured in days to capture seasonality. It was shown that the model is epidemiologically meaningful and mathematically well posed by using the results from the qualitative properties of the solution of the model. A time-dependent basic reproduction number R L t is obtained such that its yearly average is written as R ˜ L < 1 , when the disease does not invade the population (means that the number of infected humans always decreases in the seasons of transmission), and R ˜ L > 1 , when the disease remains constantly and is invading the population, and it was detected that R ˜ L ≠ R L . We also performed some evaluation of the Lassa fever disease intervention strategies using the elasticity of the equilibrial prevalence in order to predict the optimal intervention strategies that can be useful in guiding the local national control program on Lassa fever disease to make a proper decision on the intervention packages. Numerical simulations were carried out to illustrate the analytical results, and we found that the numerical simulations of the model showed that possible combined intervention strategies would reduce the spread of the disease. It was established that, to eliminate Lassa fever disease, treatments with ribavirin must be provided early to reduce mortality and other preventive measures like an educational campaign, community hygiene, isolation of infected humans, and culling/destruction of rodents must be applied to also reduce the morbidity of the disease. Finally, the obtained results gave a primary framework for planning and designing cost-effective strategies for good interventions in eliminating Lassa fever. [ABSTRACT FROM AUTHOR]

Galdeano et al. introduced the so-called information market game involving n identical firms acquiring a new technology owned by an innovator. For this specific cooperative game, the nucleolus is determined through a characterization of the symmetrical part of the core. The nonemptiness of the symmetrical( core is shown to be equivalent to one of each, super additivity, zeromonotonicity, or monotonicity. [ABSTRACT FROM AUTHOR]

We consider the dual of the generalized Erlang (n) risk model with a barrier dividend strategy. We derive integro-differential equations with boundary conditions satisfied by the expectation of the sum of discounted dividends until ruin and the moment-generating function of the discounted dividend payments until ruin, respectively. The results are illustrated by several examples. [ABSTRACT FROM AUTHOR]

Based on the single-leg air cargo issues, we establish a dynamic programming model to consider the overbooking and space inventory control problem. We analyze the structure of optimal booking policy for every kind of booking requests and show that the optimal booking decision is of threshold type (known as booking limit policy). Our research provides a theoretical support for the air cargo space control. [ABSTRACT FROM AUTHOR]

The queueing system considered is essentially a M/M/N/N queue where two types of users compete for the N resources. The users may have different arrival and service rates and are denoted as primary or secondary users. The primary users have priority access to the resources, and three levels of priority are considered: perfect priority, partial priority, and no priority. This system models the recently developed cognitive radio concept, a methodology that has been proposed for future mobile radio systems. In this context, the primary users have certain rights to use the resources, whereas the secondary users must make opportunistic use of the resources without impacting too much on the performance of the primary users. For all priority settings, the mean number of primary and secondary users is derived as are the blocking probabilities for both users. When no priority is given to the primary user, the system collapses to a truncated form of two independent M/M/8 queues. The product form solution for this special case is known, and, here, these results are given in a novel, compact form. In the case of nonzero priority, the dropping probability for the secondary users is also derived. [ABSTRACT FROM AUTHOR]