The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Antioxidant And Antiproliferative Activities Of Methanolic Extract From A Neglected Agricultural Product: Corn Cobs.

Neglected agricultural products (NAPs) are defined as discarded material in agricultural production. Corn cobs are a major waste of agriculture maize. Here, a methanolic extract from corn cobs (MEC) was obtained. MEC contains phenolic compounds, protein, carbohydrates (1.4:0.001:0.001). We evaluated the in vitro and in vivo antioxidant potential of MEC. Furthermore, its antiproliferative property against tumor cells was assessed through MTT assays and proteins related to apoptosis in tumor cells were examined by western blot. MEC showed no hydroxyl radical scavenger capacity, but it showed antioxidant activity in Total Antioxidant Capacity and DPPH scavenger ability assays. MEC showed higher Reducing Power than ascorbic acid and exhibited high Superoxide Scavenging activity. In tumor cell culture, MEC increased catalase, metallothionein and superoxide dismutase expression in accordance with the antioxidant tests. In vivo antioxidant test, MEC restored SOD and CAT, decreased malondialdehyde activities and showed high Trolox Equivalent Antioxidant Capacity in animals treated with CCl4. Furthermore, MEC decreased HeLa cells viability by apoptosis due an increase of Bax/Bcl-2 ratio, caspase 3 active. Protein kinase C expression increased was also detected in treated tumor cells. Thus, our findings pointed out the biotechnological potential of corn cobs as a source of molecules with pharmacological activity.