Probabilistic Population Modeling with Interactions between Species

Abstract

World Health Organization(WHO) instigates a continuous alertness and preparation to contain re-emergence of other variants of corona viruses. In the same vein, public welfare managements in allocating health related resources require predictive decision making, made possible through the assessment of existing health challenges. Therefore it is imperative to carryout an efficiency analysis to prioritize and determine an optimal control strategy that curtailed the transmission of COVID19 in Akwa Ibom state. In this paper, a deterministic epidemic model has been formulated using principles of Mathematical modelling of infectious diseases. This is a nonlinear system of differential equations coupled with three (3) time-varying control functionals. The control functionals are exible educational programmes, vaccination and treatment of COVID-19. The usual fuzzy-like characterization of infection severity (0 ≤ R0;Rc ≤ 1) and ( R0;Rc > 1) were achieved using the Next Generation Matrix Operator. An optimality system was derived using Pontryagin's Maximum principle, with some propositions on controllability criteria. Some forward-backward numerical solutions was executed in maple16 using validated datasets published by the Nigeria Centre for Disease Control(NCDC), peculiar to Akwa Ibom State. The efficiency analysis predicted that Strategy I (a combination of educational intervention programmes and vaccinations of the exposed and susceptible individual) as the most efficacious and optimal control strategy. Comparatively, Strategy I with 96% efficiency on reducing the infected sub-population is more effective than Strategy IV (a combination of the three control states) with efficiency index of 91%. A continuous vaccination and educational awareness programme has been recommended for community health practitioners, and compliance to these policies by the citizens can eradicate the dreaded pandemic with minimal intervention cost in the state.