SVEIRS Mathematical Model on Stability Analysis of HIV-1 Coronavirus COInfection

Abstract

Mathematical modeling has enabled epidemiologist to understand best the dynamics of infectious diseases, their impact and future predictions on their transmission and existence. Deterministic Susceptible– Vaccinated–Exposed-Infectious-Recovered (SVEIR) model on HIV-1 Coronavirus co-infection was formulated based on piecewise linear dynamical systems with constant delay. Delay here accounts for the time lapse between exposure and when the symptoms of the disease appear. Basic reproduction number 𝑅𝑜 is the threshold parameter on which the growth or reduction of the disease is based and calculated using Next Generation Matrix approach. Disease Free Equilibrium is attained when reproduction number is less or equals to one. The Disease Free Equilibrium is globally asymptotically stable whenever the reproductive number is less or equal to one and unstable otherwise and it is showed using Lyapunov function. Numerical simulation is performed using Matrix Laboratory (MatLab) dde23 solver to authenticate the analytic results. Graphical representation is then done so as to highlight on future disease dynamics and interventions. Time-delay, vaccination and chemotherapy plays a major role in stabilizing disease free equilibrium.