In this work, a general class of multi-order fractional differential equations of Lane-Emden type is considered. Here, an assumed approximate solution is substituted into a slightly perturbed form of the general class and the resulting equation is collocated at equally spaced interior points to give a system of linear algebraic equations which are then solved by suitable computer software; Maple 18.

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In this paper, we consider a deterministic model of malaria transmission. Adomian decomposition method (ADM) is used to calculate an approximation to the solution of the non-linear couple of differential equations governing the model. Classical fourth-order Runge-Kutta method implemented in Maple18 confirms the validity of the ADM in solving the problem. Graphical results show that ADM agrees with R-K 4. In order words, these produced the same behaviour, validating ADM's efficiency and accuracy of ADM in finding the malaria model solution.

In this study, Akbari-Ganji’s Method (AGM) was applied to solve Volterra Integro-Differential Difference Equations (VIDDE) using Legendre polynomials as basis functions. Here, a trial solution function of unknown constants that conform with the differential equations together with the initial conditions were assumed and substituted into the equations under consideration. The unknown coefficients are solved for using the new proposed approach, AGM which principally involves the application of the boundary conditions on successive derivatives and integrals of the problem to obtain a system of equations. The system of equation is solved using any appropriate computer software, Maple 18. Some examples were solved and the results compared to the exact solutions.

COVID-19 became a household name globally in the year 2020 after it was first discovered in Wuhan, China in December 2019. It is a global pandemic that shut the economy of all nations in the larger part of year 2020 by forcing a compulsory holiday on mankind due to its threat of mass death. The menace of this pandemic was combated with the total arsenal in human capacity. One of such weapons is case detection that leads to either self-isolation or quarantine. This weapon helps to reduce the number of new cases that may arise from undetected asymptomatic/symptomatic carriers within a population. In this article, the dynamics of COVID-19 transmission were studied by developing a mathematical model incorporating case detection, the impact of sensitization, and role of early diagnosis in curbing the spread of this disease. The basic properties in terms of existence, uniqueness, and boundedness of solution for the formulated model were discussed. Also, the model was found to exhibit two equilibrium states which are categorised as the disease-free (DFE) and pandemic equilibrium states. The reproductive number for the model was computed and used to establish the stability analysis for both equilibrium states. Center manifold theory was employed to assess the bifurcation analysis of the model and the result shows that the model exhibits forward bifurcation when the reproductive number is greater than and equal to 1.