Co-Dynamics of Trypanosomiasis and Cryptosporidiosis

In this paper a mathematical model for trypanosomiasis-cryptosporidium co-infection dynamics is investigated to give a theoretical mathematical account of the impact of cryptosporidiosis on trypanosomiasis dynamics. The model steady states are analyzed. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic basic reproduction number for the model is less than unity. The trypanosomiasis only and the cryptosporidiosis only model are each found to exhibit transcritical and backward bifurcation phenomena respectively. While the co-infection model exhibits the possibility of multiple endemic equilibria. From the sensitivity analysis, the trypanosomiasis reproductive number Rlt 0 is more sensitive to d (death due to insecticides) and crypto parameters whenever Rcr 0 \u3e 1 (crypto reproductive number). While the cryptosporidiosis reproductive number Rcr 0 is less sensitive to trypanosomiasis parameters whenever Rlt 0 \u3e 1 (trypanosomiasis reproductive number). This is an indication that cryptosporidiosis infection may be associated with an increased risk of trypanosomiasis, while trypanosomiasis infection is not associated with an increased risk for cryptosporidiosis.We incorporate time dependent controls, using Pontryagin’sMaximum Principle to derive necessary conditions for the optimal control of the disease. Furthermore, the effect of the presence of each infection on the endemicity of the other is investigated and presented numerically

Two-step low-temperature oxidation for thermal stability analysis of a combustible sphere

Thermal stability of reactive materials in a stockpile which spontaneously ignites is investigated in this article. The stockpile is modeled in a spherical domain assumed to be of a constant thermal conductivity. The energy equation is modified to a partial differential equation that is most suitable to analyze thermal stability of the combusting material. This is carried out by looking at the behavior of the temperature as selected parameters embedded in the governing equation are varied. The governing equation is solved numerically by using the Finite Difference Method (FDM). The results are given graphically and discussed appropriately to provide an understanding of the complicated combustion process. Keywords: Thermal conductivity, Low-temperature oxidation, Spontaneous ignition, Sphere, Finite Difference Metho