Pneumonia is an infection of the lungs that is caused by bacteria, viruses, fungi, or parasites. For a long time to the best of our knowledge there have not been reliable mathematical model for childhood pneumonia in Kenya. This research study developed a deterministic model based on the Susceptible-Vaccinated-Infected-Treated-Recovered-Susceptible compartment classes. The study used the partial differentiation of control reproduction number ሺܴ ሻ toinvestigate effects of; environment, efficacy of vaccination drug and treatment. Model analysis indicates the system lie in feasible region, it is bounded, has no backward bifurcation and there exists unique endemic equilibrium point when control reproduction number is greater than unity. Local and global stability of the equilibrium points indicated that control reproduction has to be maintained at less than unity to eradicate the disease. Sensitivity analysis of the control reproduction number indicates that improved vaccination drug's efficacy, attaining herd immunity, higher treatment rates and lower effects of environment are the best intervention strategies to lower impact of the pneumonia of the children under the age of five years in Kenya.

In the present paper, we formulate a new mathematical model for the dynamics of moral corruption with comprehensive age-appropriate sexual information and provision of guidance and counselling. The population is subdivided into three (3) different compartments according to their level of information on sexual matters. The model is proved to be both epidemiologically and mathematically well posed. The existence of unique morally corrupt-free and endemic equilibrium points is investigated. The basic reproduction number with respect to morally corrupt-free equilibrium is obtained using next generation matrix approach to monitor the dynamics of corrupt morals and ascertain its level in order to suggest effective intervention strategies to control this problem. The local as well as global asymptotic stability of these equilibrium points is studied. The analysis reveals a globally asymptotically stable morally corrupt-free equilibrium whenever ℛ 0 ≤ 1 and a globally asymptotically stable endemic equilibrium if otherwise. Further analysis, using center manifold theory, shows that the model exhibits forward bifurcation insinuating that the classical epidemiological requirement of ℛ 0 ≤ 1 is necessary and sufficient for elimination of moral corruption. A brief discussion on the graphical results using the available numerical procedures is shown. From numerical simulations, it was ascertain that integrated control strategy is the best approach to fight against moral corruption transmission. Lastly, some key parameters that show significance in the moral corruption elimination from the society are also exploited.

Corruption is the misuse of power or resources for private gain. This undermines economic development, political stability, and government legitimacy, the society fabric, allocation of resources to sectors crucial for development, and encourages and perpetuates other illegal opportunities. Despite Mathematical modeling being a powerful tool in describing real life phenomena it still remains unexploited in the fight of corruption menace. This study uses Lotka Volterra, predator-prey equations to develop a model to describe corruption in institutions of higher learning, use the developed model to determine its equilibria, determine the condition for stability of the equilibria and finally carry out the simulation. The corrupt students and staff act as predators while their non-corrupt counterparts act as prey in the paper. Theory of ordinary differential equations was used to determine steady states and their stability. Mathematica was used for algebraic analysis and Matlab was used for numerical analysis and simulation. Analytical result suggested multiple steady state however numerical result confirmed that the model has four steady states. Numerical bifurcation analysis suggests the possibility of backward of corrupt staff when  is about 39. Numerical simulation points to an increasing trend on corrupt staff and decrease trend on corrupt student. This study concludes that more focus should be put to staff than students in curbing the spread of corruption. Future study should strive to fit this model in real data.

A deterministic model was developed to describe the two dominant tribal coalition based voting bloc (A and B) and other tribes (C). The first order nonlinear ordinary differential equations were deduced using predator-prey equations. The system was established to lie in feasible region. The coalition free steady state was determined. The conditions necessary for local stabilities of steady states were determined using Routh-Hurwitz criteria for stability. The condition necessary for global stability of steady state were determined using Lyapunov function. The estimated numerical bound of the registered voters was obtained as 27871013. Numerical simulation was carried out using 2013 general election scenario.

COVID-19 spread in Kenya has been growing at a very high rate in the recent past. According to the Kenya's ministry of health, the confirmed COVID-19 infections as of 19 th July 2020 was 13,353 with recorded 5,122 recoveries and 234 deaths. Based on quarantine data, there is media speculation about COVID-19 manifesting gender dimension, however, no studies have been carried out to establish the gender-based dimension in the community. This paper aimed at: formulating gender based Mathematical model, estimate gender-based disease burden in the community using quarantine data and using estimated parameters and states to predict dynamics of the disease in the quarantine centers. Mathematical compartment model was developed using characteristic and status of disease. Daily number of infectious and exposed in the community was estimated using interpolating polynomials. Nonlinear least square was used to fit observed data in the developed model. Prediction of the initial value problem was carried out using MATLAB inbuilt ode solver. Daily estimate of states in Figures 8 and 9 confirms that COVID-19 is also burdening more males in the community than females. Simulation using MATLAB indicated that the number of individuals who will remain constantly infected after disease induced deaths and recoveries ranges between (567 − 219) and (363 − 116) for males and females respectively. Future studies should focus on Mathematical model analysis and predictions of disease burden in the community.