Highlights COVID-19 spread dynamics with environmental compartment is proposed. Global stability of the disease-free and endemic equilibria was obtain using Lyapunov’s function. Global sensitivity analysis was studied. A cost-effectiveness analysis presented.

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Cost-effectiveness analysis is a mode of determining both the cost and economic health outcomes of one or more control interventions. In this work, we have formulated a non-autonomous nonlinear deterministic model to study the control of COVID-19 to unravel the cost and economic health outcomes for the autonomous nonlinear model proposed for the Kingdom of Saudi Arabia. We calculated the strength number and noticed the strength number is less than zero, meaning the proposed model does not capture multiple waves, hence to capture multiple wave new compartmental model may require for the Kingdom of Saudi Arabia. We proposed an optimal control problem based on a previously studied model and proved the existence of the proposed optimal control model. The optimality system associated with the non-autonomous epidemic model is derived using Pontryagin’s maximum principle. The optimal control model captures four time-dependent control functions, thus, -practising physical or social distancing protocols; -practising personal hygiene by cleaning contaminated surfaces with alcohol-based detergents; -practising proper and safety measures by exposed, asymptomatic and symptomatic infected individuals; -fumigating schools in all levels of education, sports facilities, commercial areas and religious worship centres. We have performed numerical simulations to investigate extensive cost-effectiveness analysis for fourteen optimal control strategies. Comparing the control strategies, we noticed that; Strategy 1 (practising physical or social distancing protocols) is the most cost-saving and most effective control intervention in Saudi Arabia in the absence of vaccination. But, in terms of the infection averted, we saw that strategy 6, strategy 11, strategy 12, and strategy 14 are just as good in controlling COVID-19.

Coronavirus disease 2019 (COVID-19) pandemic has posed a serious threat to both the human health and economy of the affected nations. Despite several control efforts invested in breaking the transmission chain of the disease, there is a rise in the number of reported infected and death cases around the world. Hence, there is the need for a mathematical model that can reliably describe the real nature of the transmission behaviour and control of the disease. This study presents an appropriately developed deterministic compartmental model to investigate the effect of different pharmaceutical (treatment therapies) and non-pharmaceutical (particularly, human personal protection and contact tracing and testing on the exposed individuals) control measures on COVID-19 population dynamics in Malaysia. The data from daily reported cases of COVID-19 between 3 March and 31 December 2020 are used to parameterize the model. The basic reproduction number of the model is estimated. Numerical simulations are carried out to demonstrate the effect of various control combination strategies involving the use of personal protection, contact tracing and testing, and treatment control measures on the disease spread. Numerical simulations reveal that the implementation of each strategy analysed can significantly reduce COVID-19 incidence and prevalence in the population. However, the results of effectiveness analysis suggest that a strategy that combines both the pharmaceutical and non-pharmaceutical control measures averts the highest number of infections in the population.

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Dengue is a mosquito-borne disease which has continued to be a public health issue in Malaysia. This paper investigates the impact of singular use of vaccination and its combined effort with treatment and adulticide controls on the population dynamics of dengue in Johor, Malaysia. In a first step, a compartmental model capturing vaccination compartment with mass random vaccination distribution process is appropriately formulated. The model with or without imperfect vaccination exhibits backward bifurcation phenomenon. Using the available data and facts from the 2012 dengue outbreak in Johor, basic reproduction number for the outbreak is estimated. Sensitivity analysis is performed to investigate how the model parameters influence dengue disease transmission and spread in a population. In a second step, a new deterministic model incorporating vaccination as a control parameter of distinct constant rates with the efforts of treatment and adulticide controls is developed. Numerical simulations are carried out to evaluate the impact of the three control measures by implementing several control strategies. It is observed that the transmission of dengue can be curtailed using any of the control strategies analysed in this work. Efficiency analysis further reveals that a strategy that combines vaccination, treatment and adulticide controls is most efficient for dengue prevention and control in Johor, Malaysia.