Morufu Oyedunsi Olayiwola

The rapid transmission of COVID-19 is a vital threat to the health systems of various countries, and the need to receive the correct mathematical models to implement control measures. This paper provides a numerical analysis of an exposed compartment Caputo fractional-order SEIR model with an incubation period of SARS-CoV-2 variants. The model is nonlinear and difficult to solve analytically, so there are no precise solutions. Two methods Hermite Collocation Method (HCM) and Laplace-Adomian Decomposition Method (LADM) are used. The system is turned into nonlinear algebraic equations by HCM through Hermite polynomial expansions whereas LADM uses Laplace transforms and Adomian polys to deal with nonlinearities. Simulations of the Maple indicate that the two methods can effectively estimate the dynamics of the fractional SEIR, although HCM is more accurate and converges more quickly. Fractional-order formulation also includes the effects of memory in the transmission of the disease. This evidence proves that the application of fractional-order modeling with Hermite based numerical methods provides a strong platform through which the dynamics, especially the epidemiological ones, may be analyzed and the adaptive public health responses may be directed.

This study employed a mathematical model to evaluate how seasonal variations, vector dispersal, and mobility of people affect the spread of the Zika virus. The model's positive solutions, invariant zones, and solution existence and uniqueness were validated through proved theorems. The equilibria points were identified, and the basic reproduction number was calculated. The model was semi-analytically solved using a modified homotopy perturbation approach, and an applied convergence test proved that the solution converges. The simulation results indicated that under optimal breeding conditions, the density of healthy mosquitoes peaked in the fourth month. Two months later, increased mosquito dispersal and human carriers facilitated by favorable weather led to a rise in mosquito infectiousness, peaking between the fourth and eighth months due to significant seasonal effects, resulting in high Zika transmission. To effectively control mosquito populations and reduce Zika transmission, it is recommended that public health interventions focus on the critical periods spanning the third to eighth months.

This research aims to evaluate the impact of the COVID-19 pandemic on stock markets in Africa. The study analyzes the stock market returns in nine selected African countries (South Africa, Morocco, Tunisia, Botswana, Nigeria, Uganda, Kenya, Mauritius, and Tanzania) before, during, and after the COVID-19 pandemic. We investigate the impact of COVID-19 on stock market returns and the effect of the worst-hit country's volatility on other African countries' stock market returns utilizing autoregressive conditional heteroscedasticity (ARCH), generalized ARCH (GARCH), and threshold ARCH (TARCH) tests. Additionally, we explore the implications for foreign investors in terms of portfolio diversification and risk management, contributing to the existing literature on the effects of the COVID-19 crisis on financial markets and investment risk. Thereby, we provide insights into African stock markets' interconnectedness and help foreign investors reduce their losses and manage risks associated with the COVID-19 pandemic. Finally, we discuss the need for further research.