Abstract
There have been a number of different intervention strategies introduced and studied
to fight the COVID-19 virus spread since its inception. These include COVID-
19 vaccines and various non-pharmaceutical interventions such as practising social
distancing, banning of public events and lockdown policies. Nutrition is
one of the non-pharmaceutical interventions that could contribute in mitigating
the COVID-19 virus spread. In this study we present a mathematical modelling
framework to investigate the optimal impact of nutrition on the COVID-19 virus
spread in South Africa. To do so, we considered a seven-state model and use
the administration of nutrition as the control variable from optimal control analysis.
The model without control was analysed using mathematical theories to
establish the existence and uniqueness of the solutions, the existence and stability
of the equilibrium points and the effective reproduction number (Re f f ) was
determined. The optimal control problem and four objective functions were formulated
and the characteristic of the control variable, u1, were presented. The first
objective function consist of all the four infectious classes in our system, the malnourished
symptomatically infected, well-nourished symptomatically Infected,
malnourished asymptomatically infected and well-nourished asymptomatically
infected class. The second objective consist of malnourished symptomatically
infected and malnourished asymptomatically infected class, the third objective
function considers malnourished symptomatically infected and well-nourished
asymptomatically infected class, and the fourth objective function consist of the
malnourished asymptomatically infected and well-nourished symptomatically In-
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fected class. The numerical findings show that the first objective function gives
the best results in reducing the spread of the COVID-19 virus compared to the
other 3 objective functions.