This paper work was designed to study the effect of treatment on the transmission of pneumonia infection. When studying the transmission dynamics of infectious diseases with an objective of suggesting control measures, it is important to consider the stability of equilibrium points. In this paper, basic reproduction number, effective reproduction number, existences and stability of the equilibrium point were established.Using Lyaponov function we discovered that the disease free equilibrium is unstable. The results are presented in graphs and it is discovered that the spread of the infection will be greatly affected by the rate of treatment and natural immunity.

We study a one dimensional non-linear model of multi-layered human skin exposed to microwave heating during cancer therapy. The model is analyzed using homotopy perturbation method and the fact that there are variations in specific heat, thermal conductivity and blood perfusion from one individual to another were considered. The purpose of this study was to investigate the effect of variable blood perfusion, microwave heating and thermal conductivity on the temperature field during microwave hyperthermia. By varying the parameters, we were able to determine maximum rise of temperature as an individual undergoes cancer therapy. The results were presented in graphs and it was discovered that the temperature of the tumor increases with increase in the microwave heating index while the blood perfusion remain constant.

Globally, the COVID-19 presents a serious concern to the wellbeing of people. COVID-19 was first detected in Wuhan, China. The disease became a source of concern for Nigerians after the country registered its first case in February 2020. Currently, the country has recorded 255,103 confirmed cases, 249,246 recovered cases, and 3,142 deaths as of March 21, 2022. We proposed a SEQIHRV model to investigate the spread of coronavirus disease in Nigeria. This model defines the infection dynamics' transmission routes as well as effect of contaminated surfaces on the human population. Unfortunately, the virus's propagation and mortality from COVID-19 is increasing daily. Therefore, it is required to manage and control the flow of the infection. The impact of control measures as time-dependent interventions was investigated in this study utilizing optimization technique to determine their effects on the spread of Corona virus. The basic reproduction was calculated and used to calcite the sensitive parameters affecting the system, which revealed the key parameters leading to COVID-19 propagation. The control optimization of the sytem was performed using Pontryagin's maximum principle to determine the best approach for controlling the spread. The discoveries from the simulation showed that the combination of all four control approaches will help to reduce infection to zero in the population.

In this research, we proposed the fusing of Elzaki transform and projected differential transform (PDTM) to obtain an analytical or approximate solution of the Rosenau-Hyman and Korteweg-de Vries equations which respectively govern pattern formation in liquid drops and model of waves on shallow water surfaces. The results obtained presented in tables and graphs showed better efficiency, accuracy, and convergence of the method to handle Rosenau-Hyman and Korteweg-de Vries equations when compared to other methods in the literature. Keywords:          Rosenau-Hyman Equation; Korteweg-de Vries equation; Elzaki Projected differential transform method; Semi-analytic approach

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