Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of infectious individuals in a community/nation. In this paper, a nonlinear deterministic model with time-dependent controls has been proposed to describe the dynamics of bacterial meningitis in a population. The model is shown to exhibit a unique globally asymptotically stable disease-free equilibriumE0, when the effective reproduction numberRVT≤1, and a globally asymptotically stable endemic equilibriumE1, whenRVT>1; and it exhibits a transcritical bifurcation atRVT=1. Carriers have been shown (by Tornado plot) to have a higher chance of spreading the infection than those with clinical symptoms who will sometimes be bound to bed during the acute phase of the infection. In order to find the best strategy for minimizing the number of carriers and ill individuals and the cost of control implementation, an optimal control problem is set up by defining a Lagrangian functionLto be minimized subject to the proposed model. Numerical simulation of the optimal problem demonstrates that the best strategy to control bacterial meningitis is to combine vaccination with other interventions (such as treatment and public health education). Additionally, this research suggests that stakeholders should press hard for the production of existing/new vaccines and antibiotics and their disbursement to areas that are most affected by bacterial meningitis, especially Sub-Saharan Africa; furthermore, individuals who live in communities where the environment is relatively warm (hot/moisture) are advised to go for vaccination against bacterial meningitis.

Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized ( p , q )-Mathieu type series. Then, their composition formulas by using the integral transforms are introduced. Further, a new generalized form of the fractional kinetic equation involving the series is also developed. The solutions of fractional kinetic equations are presented in terms of the Mittag-Leffler function. The results established here are quite general in nature and capable of yielding both known and new results.

The aim of the present paper is to develop a new generalized form of the fractional kinetic equation involving a generalized k-Mittag-Leffler function \(E^{\gamma,\rho}_{k,\zeta,\eta}(\cdot)\). The solutions of fractional kinetic equations are discussed in terms of the Mittag-Leffler function. Further, numerical values of the results and their graphical interpretation is interpreted to study the behavior of these solutions. The results established here are quite general in nature and capable of yielding both known and new results.

AES (Advanced Encryption Algorithm) is a block cipher, which is world wide implemented for encryption of data. It has been accepted as a standard for data security since 2001. AES is a substitution and permutation cipher, which provides confusion by using substitution box (S-Box) in the algorithm. The main drawback of AES is that it uses static S-Box throughout algorithm, which compromise the security of AES and may be exposed to different algebraic attacks. So to overcome this problem new Dynamic AES algorithm developed by key dependent dynamic S-Box using dynamic irreducible polynomial and affine constant. The analysis is done on gray scale and colour images. Both the images are encrypted and decrypted by using standard AES and Dynamic AES. Quality of algorithm and the level of security is analyzed based on the parameters like Image Histogram Analysis, Adjacent Pixel Correlation Analysis, Image Entropy, Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Encryption Quality.