Ephraim Agyingi

A mathematical model of the compression of a spinal disc

A model is developed of the stress-strain response of an intervertebral disc to axial compression. This is based on a balance of increased intradiscal pressure, resulting from the compression of the disc, and the restraining forces generated by the collagen fibres within the annulus fibrosus. A formula is derived for predicting the loading force on a disc once the nucleus pressure is known. Measured material values of L3 and L4 discs are used to make quantitative predictions. The results compare reasonably well with experimental results.

Thermal detection of a prevascular tumor embedded in breast tissue.

This paper presents a mathematical model of heat transfer in a prevascular breast tumor. The model uses the steady state temperature of the breast at the skin surface to determine whether there is an underlying tumor and if so, verifies whether the tumor is growing or dormant. The model is governed by the Pennes equations and we present numerical simulations for versions of the model in two and three dimensions.

A Quantitative Model of Cutaneous Melanoma Diagnosis Using Thermography

Cutaneous melanoma is the most commonly diagnosed cancer and its incidence is on the rise worldwide. Early detection and differentiation of a malignant melanoma from benign cutaneous lesions provides an excellent chance for treating the disease. Thermography is a non-invasive tool that can be used to detect and monitor skin lesions. We model heat transfer in a skin region containing a lesion. The model which is governed by the Pennes equation uses the steady state temperature at the skin surface to determine whether there is an underlying lesion. Numerical simulations from the model ascertain whether the lesion is malignant or benign.

The dynamics of multiple species and strains of malaria

This paper presents a deterministic SIS model for the transmission dynamics of malaria, a life-threatening disease transmitted by mosquitos. Four species of the parasite genus Plasmodium are known to cause human malaria. Some species of the parasite have evolved into strains that are resistant to treatment. Although proportions of Plasmodium species vary considerably between geographic regions, multiple species and strains do coexist within some communities. The mathematical model derived here includes all available species and strains for a given community. The model has a disease-free equilibrium, which is a global attractor when the reproduction number of each species or strain is less than one. The model possesses quasi-endemic equilibria; local asymptotic stability is established for two species, and numerical simulations suggest that the species or strain with the highest reproduction number exhibits competitive exclusion.

Modeling the effect of topical oxygen therapy on wound healing

Oxygen supply is a critical element for the healing of wounds. Clinical investigations have shown that topical oxygen therapy (TOT) increases the healing rate of wounds. The reason behind TOT increasing the healing rate of a wound remains unclear and hence current protocols are empirical. In this paper we present a mathematical model of wound healing that we use to simulate the application of TOT in the treatment of cutaneous wounds. At the core of our model is an account of the initiation of angiogenesis by macrophage‐derived growth factors. The model is expressed as a system of reaction‐diffusion equations. We present results of simulations for a version of the model with one spatial dimension.

Stability and Hopf bifurcation of a two species malaria model with time delays

We present a mathematical model of the transmission dynamics of two species of malaria with time lags. The model is equally applicable to two strains of a malaria species. The reproduction numbers of the two species are obtained and used as threshold parameters to study the stability and bifurcations of the equilibria of the model. We find that the model has a disease free equilibrium, which is a global attractor when the reproduction number of each species is less than one. Further, we observe that the non-disease free equilibrium of the model contains stability switches and Hopf bifurcations take place when the delays exceed the critical values.