Approximate Solution of the Fractional Order Mathematical Model on the Transmission Dynamics on The Co-Infection of COVID-19 and Monkeypox Using the Laplace-Adomian Decomposition Method (Published)
A fractional order compartmental model on the transmission dynamics of the co-infection of COVID-19 and Monkeypox is presented. The approximate solutions of the fractional order model are obtained using the Laplace-Adomian Decomposition method in the form of an infinite series which was shown to converge to the exact value. Using the MATLAB fmincon algorithm, we carried out a data fitting analysis using real life COVID-19 and Monkeypox data so as to obtain estimates for some of the key parameters used in the formulation of model. The results of our analysis showed that an increase in the effective treatment capacity in the human population will significantly reduce the burden of these diseases in the human population.
Keywords: Approximate solution, Transmission dynamics, fractional order mathematical model, laplace-adomian decomposition method, monkeypox, the co-infection of COVID-19
Mathematical Assessment of the Transmission Dynamics of HIV/AIDS with Treatment Effects (Published)
This article examines the transmission dynamics of HIV/AIDS with treatment effects. The total population ( ) was grouped into four compartments namely susceptible individuals at time t ( ), infected humans at time t ( ), individuals on treatment at time t ( ), and the AIDS carriers at time t ). A first order deterministic mathematical model for the case is formulated and analyzed to gain insight into the qualitative features of the local stability and disease free equilibrium which enable us to understand the transmission dynamics of the disease. The numerical simulation of the model was carried out to investigate the sensitivity of some threshold parameters on spread rate of the disease. We also investigated the impact of early detection of HIV cases and compliant behavior of patients on treatment. Our results from numerical simulation and early detection of HIV case/ compliant behavior of patients on treatment show that early detection of HIV case and compliant behavior of patients on treatment reduce spread of the disease and minimize rate at which people develop AIDS.
Keywords: HIV/AIDS, Modeling, Transmission dynamics, Treatment., mathematical assessment