Background Dengue is a vector-borne viral disease endemic in Malaysia. The disease is presently a public health issue in the country. Hence, the use of mathematical model to gain insights into the transmission dynamics and derive the optimal control strategies for minimizing the spread of the disease is of great importance. Methods A model involving eight mutually exclusive compartments with the introduction of personal protection, larvicide and adulticide control strategies describing dengue fever transmission dynamics is presented. The control-induced basic reproduction number (R˜0) related to the model is computed using the next generation matrix method. Comparison theorem is used to analyse the global dynamics of the model. The model is fitted to the data related to the 2012 dengue outbreak in Johor, Malaysia, using the least-squares method. In a bid to optimally curtail dengue fever propagation, we apply optimal control theory to investigate the effect of several control strategies of combination of optimal personal protection, larvicide and adulticide controls on dengue fever dynamics. The resulting optimality system is simulated in MATLAB using fourth order Runge-Kutta scheme based on the forward-backward sweep method. In addition, cost-effectiveness analysis is performed to determine the most cost-effective strategy among the various control strategies analysed. Results Analysis of the model with control parameters shows that the model has two disease-free equilibria, namely, trivial equilibrium and biologically realistic disease-free equilibrium, and one endemic equilibrium point. It also reveals that the biologically realistic disease-free equilibrium is both locally and globally asymptotically stable whenever the inequality R˜0<1holds. In the case of model with time-dependent control functions, the optimality levels of the three control functions required to optimally control dengue disease transmission are derived. Conclusion We conclude that dengue fever transmission can be curtailed by adopting any of the several control strategies analysed in this study. Furthermore, a strategy which combines personal protection and adulticide controls is found to be the most cost-effective control strategy.
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.
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.