In this paper we discuss the tumor growth of GB (Glioblastoma) with piecewise constant arguments represented in the following equation \ndx(t)/dt=x(t)r(1-αx(t)-β_0 ⟦t⟧x(⟦t⟧)-β_1 ⟦t-1⟧x(⟦t-1⟧))-γ_1 ⟦t⟧x(t)x(⟦t⟧)-γ_2 ⟦t-1⟧x(t)x(⟦t-1⟧),\nwhere the parameters α,β_0,β_1,γ_1 ,γ_(2 )and r belong to R^+ and ⟦t⟧ is the integer part of t∈[0,∞). The parameter γ_1 represents the effect of the treatment on the tumor, while γ_2 is embedded to show the rate that causes a negative effect from the immune system to the tumor population. We embed ⟦t⟧ and ⟦t-1⟧ as coefficients to the equation to emphasize the treatment therapy for specific time. We investigate some theoretical results on the local and global stability of the positive equilibrium point. In addition, we prove that the discrete equation undergoes period doubling (flip) and Neimark-Sacker bifurcation. For an early detection of Glioblastoma, we incorporate an Allee function of time t to analyze the behavior for a strong Allee effect. Numerical simulations are performed to validate the theoretical results.
In this study, monoclonal population growth with piecewise constant arguments is modeled, where ⟦t⟧ and ⟦t-1⟧ are embedded as coefficients to equation (A) to emphasize the population growth for specific times such as\ndx(t)/dt=x(t)r(1-αx(t)-β_0 ⟦t⟧x(⟦t⟧)-β_1 ⟦t-1⟧x(⟦t-1⟧)). (A)\nThe parameters α,β_0,β_1 moreover, r belongs to R^+ and ⟦t⟧ is the integer part of t∈[0,∞). Parameter r is the population growth rate of the monoclonal tumor, while α,β_0 and β_1 are rates for the delayed tumor volume that based on the logistic population model. In order to analyze the dynamic behavior of the equation (A), we study the conditions for local and global stability. In addition, it is proven that the discrete equation undergoes period doubling (flip) and Neimark-Sacker bifurcation. For early detection of monoclonal tumor growth, we incorporate an Allee function of time t and analyze the behavior for a strong Allee effect.
ABSTRACT\n\n\nMethanol extract was prepared from Alhagi maurorum and evaluated for its potential antiulcerogenic and hepatoprotective effects in rats. Preliminary phytochemical analysis and acute LD50 were also carried out. Oral administration of the methanol extract (400 and 800 mg kg-1) of Alhagi maurorum significantly (P<0.05) decreased the average ulcer index in a dose dependent manner with a curative ratio of 69.6 and 74.6% for the small and large dose respectively, in the ethanol-induced gastric ulceration. Based on the decreased ulcer index, Alhagi maurorum induced significant antiulcerogenic effect against aspirin-induced gastric ulceration with a curative ratio of 90.3 and 85.6% respectively. The number of ulcers and total acidity were significantly (P<0.01) decreased. Improvement of the histopathological picture of liver tissue and the serum biochemical parameters (AST, ALT, GGT and Albumin) indicated that a good hepatoprotective effect against CCl4-induced hepatotoxicity was achieved by oral administration of methanol extract of Alhagi maurorum. No symptoms of discomfort were reported after doses of up to 2.5 g kg-1. Methanol extract of Alhagi maurorum was reported to contain unsaturated sterols, triterpenes, tannins, flavonoids and carbohydrates and/or glycosides as active constituents. GC-Ms analysis revealed the presence of\n\n24 compounds of which Luteolin (14.88%), Amarogentin (23.22%), Palmitic acid (24.23%), inoleic acid (6.6%) are major constituents. This study proved that the methanol extract of Alhagi maurorum has a promising gastro- and hepatoprotective effect in rats.
The susceptibility of the third larval instar of the Oryctes agamemnon to infection and subsequent death by exposure to three native entomopathogenic fungi (NEPF); Beauveria bassiana, Metarhizium anisopliae and Lecanicillium lecanii was determined. Three concentrations of each NEPF isolate were used for dose-response mortality against the 3rd larval instar. Mortality rates of the larvae reached 34.2, 48.1 and 55.5% at the concentrations (104, 106 and 108 conidia/ml) of B. bassiana. M. anisopliae recorded mortalities reached 39.5, 57.4 and 60.8% to the target larvae. Similarly, the accumulated mortality of the 3rd instar larvae recorded 17.4, 26.4 and 29.2% for L. lecanii. The LT50 values of the 3rd instar of O. agamemnon larvae recorded 9.9 and 11.3 days for the two concentrations that achieved 50% mortality for B. bassiana and M. anisopliae respectively. M. anisopliae was the most efficient one, followed by B. bassiana and L. lecanii. The proteolytic activity of the three NEPF was investigated under different factors (incubation periods, temperature and pH). The results showed that the maximum activity of protease produced by B. bassiana, L. lecanii and M. anisopliae was recorded after 6 days of incubation with 28°C incubation temperature in the medium initially adjusted to pH 6.
