Abstract
The emergence of the COVID-19 pandemic has been a major social and economic challenge globally. Infections from infected surfaces have been identified as drivers of Covid-19 transmission, but many epidemiological models do not include an environmental component to account for indirect transmission. We formulate a deterministic Covid-19 model with both direct and indirect transmissions. The computed basic reproduction number R0 represents the average number of secondary direct human-to-human infections, and the average number of secondary indirect infections from the environment. Using Partial Rank Correlation Coefficient, we compute sensitivity indices of the basic reproductive number R0 . As expected, the most significant parameter to reduce initial disease transmission is the natural death rate of pathogens in the environment. Variation of the basic reproduction number for different values of direct and indirect transmissions are numerically investigated. Decreasing the effective direct human-to-human contact rate and indirect transmission from human-to-environment will decrease the spread of the disease as R0 decreases and vice versa. Since the effective contact rate often accounted for as a factor of the force of infection and other interventions measures such as treatment rate are prominent features of infectious diseases, we consider several functional forms of the incidence function, and numerically investigate their potential impact on the long-term dynamics of the disease. Simulations results revealed some differences for the time and infection to reach its peak. Thus, the choice of the functional form of the force of infection should mainly be influenced by the specifics of the prevention measures being implemented.