J. B. Shukla¹, Shikha Singh², Jitendra Singh², Sunil Kumar Sharma^3,*

CMC-Computers, Materials & Continua, Vol.68, No.2, pp. 1859-1875, 2021, DOI:10.32604/cmc.2021.012095

Abstract In this research, we proposed a non-linear SIS model to study the effect of variable interaction rates and non-emigrating population of the human habitat on the spread of bacteria-infected diseases. It assumed that the growth of bacteria is logistic with an intrinsic growth rate is a linear function of infectives. In this model, we assume that contact rates between susceptibles and infectives as well as between susceptibles and bacteria depend on the density of the non-emigrating population and the total population of the habitat. The stability theory has been analyzed to analyzed to study the crucial role played by bacteria… More >

Avaneesh Singh^*, Saroj Kumar Chandra, Manish Kumar Bajpai

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.3, pp. 967-990, 2020, DOI:10.32604/cmes.2020.011601

Abstract COVID-19 disease has emerged as one of the life threatening threat to the society. A novel beta coronavirus causes it. It began as unidentified pneumonia of unknown etiology in Wuhan City, Hubei province in China emerged in December 2019. No vaccine has been produced till now. Mathematical models are used to study the impact of different measures used to decrease pandemic. Mathematical models have been designed to estimate the numbers of spreaders in different scenarios in the present manuscript. In the present manuscript, three different mathematical models have been proposed with different scenarios, such as screening, quarantine, and NPIs, to… More >

Yan Cai^1,1, Zhiyong Li^1,2,*

Molecular & Cellular Biomechanics, Vol.14, No.2, pp. 59-81, 2017, DOI:10.3970/mcb.2017.014.057

Abstract To investigate the dynamic changes of solid tumor and neo-vasculature in response to chemotherapeutic agent, we proposed a multi-discipline three-dimensional mathematical model by coupling tumor growth, angiogenesis, vessel remodelling, microcirculation and drug delivery. The tumor growth is described by the cell automaton model, in which three cell phenotypes (proliferating cell, quiescent cell and necrotic cell) are assumed to reflect the dynamics of tumor progress. A 3D tree-like architecture network with different orders for vessel diameter is generated as pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are calculated… More >

Yan Cai^1,2,3, Jie Wu⁴, Zhiyong Li^1,2

Molecular & Cellular Biomechanics, Vol.12, No.4, pp. 231-248, 2015, DOI:10.3970/mcb.2015.012.231

Abstract We propose a coupled mathematical model for the detailed quantitative analyses of initial microtumour and micrometastases formation by including cancer cell migration, host vessel cooption and changes in microenvironment. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. Migration probability of a migrating cell is assumed to be influenced by local chemical microenvironment. Pre-existing vessel cooption and remodelling are introduced according to the local haemodynamical microenvironment, such as interstitial pressure and vessel wall permeability. After the tumour cells and tumour vessels distribution are updated, the chemical substances are coupled calculated with the… More >

Arzu Turan Dincel¹, Surkay D. Akbarov^2,3

CMC-Computers, Materials & Continua, Vol.53, No.3, pp. 249-270, 2017, DOI:10.32604/cmc.2017.053.265

Abstract This paper deals with the mathematical modelling and 3D FEM study of the energy release rate (ERR) in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes. The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located. After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal… More >