| dc.description.abstract | The coronavirus disease 2019 (COVID-19) is caused by the severe acute respira-
tory syndrome coronavirus-2 (SARS-CoV-2). The virus is primarily transmitted
to humans through inhaling respiratory droplets produced by sneezing, coughing,
and conversing closely with an infectious person (direct transmission) or indirectly
through contact with contaminated surfaces (indirect transmission). To Prevent
and control the fast spreading of COVID-19, health providers and governments
around the world have used containment measures such as lockdown, travel bans,
cessation of movement, social distancing, proper hygiene, and hand sanitization,
among others. Despite these safeguards, the virus continues to spread, although
at a slower rate. The disease is linked to a range of infectious periods and hu-
man movement (di usion). Vaccination has proved to be e ective in minimising
the severity of the disease. Most of the COVID-19 dynamics models so far done
have employed a constant coe cient of transmission, whereas infectiousness of an
individual varies with time. Thus, an SEIR model is developed to assess the e ect
of the varying transmission coe cient in the dynamics of COVID-19. The model
solutions were checked for well-posedness to ensure that they are both positive and
bounded. The next generation matrix approach is applied to determine the e ective
reproduction number, R!. The bifurcation analysis showed that when the trans-
mission coe cient > then R! > 1 and the disease would spread, otherwise
the disease will die out. The numerical simulation showed that reducing the trans-
mission coe cient would curtail the spread of infection. The existing COVID-19
di usive models do not establish the minimum travelling wave speed that connects
the Disease Free Equilibrium (DFE) and the Endemic Equilibrium (EE) enabling
infection. Thus, a di usive COVID-19 model is developed and analyzed to assess
the e ect of human movement. Existence of travelling wave solutions of the model
are shown. Exact solutions to the traveling wave are computed using the Tangent
hyperbolic method (Tanh Method). Faced with the inadequate supply of COVID-
19 vaccines especially in developing world, it is imperative to determine the critical
mass to be vaccinated so as to attain herd immunity. Thus, a COVID-19 model in-
corporating vaccination is developed and analyzed. Sensitivity analysis done with
respect to key parameters of the vaccine reproduction number, RV , indicates that
control strategies should target increasing the rate of vaccination with high e cacy
vaccines. The study results suggest that a high rate of vaccination (
) and high
e cacy vaccine (#) are critical in achieving herd immunity also known as 'popula-
tion immunity' and control disease spread within the population. Optimal control
analysis shows that an optimal infection control is achieved by increasing the rate
of vaccination and reducing infection by administering a high e cacy vaccine, thus
reducing the probability of transmission. Numerical simulations show that when
vaccination rates and vaccine e cacy are high, the number of infections fall sharply.
The ndings of this study highlight the signi cance of interventions and in partic-
ular the speci c targets for health care providers in mitigating the transmission of
COVID-19. | en_US |
