Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures.

To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as " R 0 ", to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana-Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes.

Influence of Mineral Fertilizer and Manure Application on the Yield and Quality of Maize in Relation to Intercropping in the Southeast Republic of Kazakhstan.

Maize (Zea mays L.) is a valuable forage crop. It is also an essential and promising crop for the Republic of Kazakhstan, cultivated in the southern zone. Some new maize hybrids have been introduced, which have been beneficial for high yields with less fertilizer input. This study aims to introduce the new maize hybrid, Arman 689, for the judicial use of fertilizer and the high yield. This study was carried out in 2015 in the southeast region of Kazakhstan. There are five treatments with various mineral fertilizer and poultry manure doses: 1. control (T0), 2. P60 K100 (T1), 3. N100P60K100 (T2). 4. N100P60K100 + 40 tons of manure/ha (T3), and 5. N100P60K100 + 60 ton of manure/ha (T4). The fertilizers used were ammonium nitrate (N­34.6%), amorphous (N­11.0%, P2O5­46.0%), and potassium chloride KCl (K2O­56%). The results showed that the grain yield ranges from 5.51 t/ha (T0) to 8.49 (T4) t/ha. The protein contents in the maize grain varied from 9%(T0)−11.3%(T4). The grain nitrogen content accounted for 54.2 to 52.0%. The nutrient uptake results by different treatments indicated that nitrogen contributed to 41.5% of the total yield increase. Using manure in combination with mineral fertilizers reduced the payback of the applied resources, as the payback of T2−T4 was 8.8−9.1 kg of grain. With the application of recommended mineral fertilizer (NPK), the protein yield was 0.83 t/ha, 0.33, and 1.22 t/ha higher than T0 and T1 treatments, respectively. There was no significant yield difference under T3 and T4 treatments (p > 0.05). Overall, the treatment, NPK + 40 tons of manure, was proved the ultimate for the Arman hybrid in providing the optimum quantity and quality of maize, as well as reducing the payback cost (8.8−9.1 kg of grain). It is suggested to apply NPK-recommended doses along with manure in maize (Arman hybrid)-based intercropping systems to utilize the resources efficiently.