Sterile insect technology (SIT) is an environmental-friendly method which depends on the release of sterile male mosquitoes that compete with the wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring and as such reduces the population of Zika virus vector population over time, thereby eliminating the spread of Zika virus in a population. The fractional order sterile insect technology (SIT) model to reduce the spread of Zika virus disease is considered in this present work. We employed the use Laplace–Adomian decomposition method (LADM) to determine an analytical (approximate) solution of the model. The Laplace–Adomian decomposition method (LADM) produced a solution in form of an infinite series that further converges to the exact value. We compared solutions of the fractional model with the classical case using our plots and discovered that the fractional order has more degree of freedom and as such the system can be varied to get many preferred responses of the different classes of the model as the fraction (β) could be varied to the desired rate, say 0.7, 0.4, etc. We have been able to show that LADM can be used to solve an SIT model which has never been done before in literature.

The introduction of Global System for Mobile Communication (GSM) in Nigeria is responsible for significant tremendous teledensity ratio increment, which results in network congestion in most busy areas. In this paper, we applied a Second Order Necessary Condition (a Mathematical Optimization Technique) as a tool in solving the problem of network congestion. One of the GSM providers; Mobile Telecommunication of Nigeria (MTN), was used to demonstrate the usefulness of Second Order Necessary Condition to the control of network congestion at Michael Okpara University of Agriculture, Umudike (MOUAU). Free flow of connection between mobile phone users at different locations within the area of investigation was established, hence congestion controlled.

In this paper, number of conjugacy classes and irreducible characters in a non-abelian group of order $2^6$ are investigated using cycle pattern of elements. Through the exploits of commutator and representation of elements as a product of disjoint cycles, the number of conjugacy classes is obtained which extends some results in literature.

HIV/AIDS is a dreaded disease which has over the years claimed the life of so many people both female and male, adult and children in the whole continents or the globe. In this paper, a mathematical model on the control of HIV/AIDS was formulated using; vaccine, condom, therapeutic dose and public health campaign as control measures. The dynamic analysis of the model was carried out and the effective reproduction number R0 obtained. The local and global stability analyses were conducted. From the analysis carried out, we got that R0>1, which shows that HIV/AIDS is endemic. Furthermore, the Maple software was applied to obtain the eigenvalues which validate the asymptotically stable nature of the disease equilibrium position. Matlab was used to simulate various submodels from the main model using numerical values of the parameters. Results obtained were discussed which extends some results in literature.

This paper investigates the impact of the various parameters of the mathematical model for Hepatitis B virus-Hepatitis D virus (HBV-HDV) co-infection with controls (awareness, vaccine and therapy). It establishes that the model is biologically meaningful and epidemiologically well posed. Furthermore, simulations are carried out on the equations of the model using MATLAB and the results indicate that; when c 1 (awareness) increase from 0.08 to 0.70, then the number of exposed HB individuals in the population will also increase. Conversely, we notice a drastic decrease in the number of exposed HBD individuals in the population when c 1 (awareness) increase from 0.08 to 0.70. Again, we observe a decrease in the number of exposed treated individuals in the population when c(therapy) increase from 0.08 to 0.50. Similarly, we notice an increase in the number of recovered HBD individuals in the population upon the increase of c(therapy) from 0.08 to 0.50. We therefore conclude that awareness, vaccine and therapy are good measure which can be used to effectively control HBV-HDV co-infection in a population. However, awareness and vaccine are better control strategies than therapy. Hence, these simulation results provide the best framework for the control of the disease; Hepatitis B virus-Hepatitis D virus (HBV-HDV) co-infection in a population.