The term corruption refers to the process that involves the abuse of a public trust or office for some private benet. Corruption becomes a threat to national development and growth especially when there is no political will to fight it. Prevention and disengagement initiatives are part of EACC strategies used to fight corruption. Prevention strategies aim to stop or discourage citizens from engaging in corruption. Disengagement strategies attempt to reform corrupt individuals and to reclaim the stolen resources back to the public kitty. We describe prevention and disengagement strategies mathematically using an epidemiological compartment model. The prevention and disengagement strategies are modeled using model parameters. The population at risk of adopting corrupt ideology was divided into three compartments: S(t) is the susceptible class, C(t) is the Corrupted class, and M(t) is the corrupt political/sympathersizer class. The model exhibits a threshold dynamics characterised by the basic reproduction number R0. When R0 < 1 the system has a unique equilibrium point that is asymptotically stable. For R0 > 1, the system has additional equilibrium point known as endemic, which is globally asymptotically stable. These results are established by applying lyapunov functions and the LaSalles invariance principle. Based on our model we assess strategies to counter corruption vice.
We propose a deterministic model that describes the dynamics of students who have the capabilityWe propose a deterministic model that describes the dynamics of students who have the capabilityto perform well in mathematics examinations and engage in careers that demand its applicationand the negative inuence of individuals with mathematics anxiety on the potential students.Our model is based on SIR classical infectious model classes with Susceptible (S) and Infected (I)taken as Math anxious students (Ax) and Removed (R) adopted as achievers students (Aa) . Themodel is shown to be both epidemiologically and mathematically well posed. In particular, weprove that all solutions of the model are positive and bounded; and that every solution with initialconditions in remains in the set for all time. The existence of unique math anxious-freeand endemic equilibrium points is proved and the basic reproduction number R0 computed usingnext generation matrix approach. A global stability of anxious-free and the endemic equilibria areperformed using Lasselles invariance principle of Lyapunov functions. Sensitivity analysis showsthat achievement rate of potential achievers and achievement rate of math anxious students are the most sensitive parameters. This indicates that effort should be directed towards theseparameters, by having well trained mathematics staff and the best printed and technological resources so as to control the spread of mathematics anxiety. Furthermore, scaling up the understanding level of mathematics algorithms, lowers the mathematics anxiety level and consequently, the spread of mathematics anxiety amongst students reduces. Lastly, some numerical simulations are performed to verify the theoretical analysis result using Matlab software.
Cholera is an infection of the small intestine of humans caused by a gram-negative bacterium called Vibrio cholerae. It is spread through eating food or drinking water contaminated with faeces from an infected person. It causes rapid dehydration and general body imbalance, and can lead to death since untreated individuals suer severely from diarrhea and vomiting. Its dynamics involves multiple interaction between the human host, the pathogen and the environment which contributes to both human to human and indirect environment to human transmission pathways. Rehydration is critical in reducing cholera death. This has been studied by other scholars but they did not consider delay in rehydration on the spread of cholera. In this paper, I formulate a mathematical model based on system of ordinary differential equation with rehydration on the spread of cholera in a logistically growing population. The existence of the steady states and the basic reproduction number is established such that disease free equilibrium point exists. Determination of endemic equilibrium shows that the model has positive points. The findings will be signicant in the sense that timely rehydration should be done during cholera outbreak and will enable individuals with symptoms to seek immediate medical attention.
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