Vector-host infectious diseases remain a challenging issue and cause millions of deaths each year globally. In such outbreaks, many countries especially developing or underdevelopment faces a situation where the number of infected individuals is getting larger and the medical facilities are limited. In this paper, we construct an epidemic model to explore the transmission dynamics of vector-borne diseases with nonlinear saturated incidence rate and saturated treatment function. This type of incidence rate, as well as the saturated treatment function, is also known as the Holling type II form and describes the effect of delayed treatment. Initially, we formulate a mathematical model and then present the basic analysis of the model including the positivity and boundedness of the solution. The threshold quantity R 0 is presented and the stability analysis of the system is carried out for the model equilibria. The global stability results are shown using the Lyapunov function of Goh-Voltera type. The existence of backward bifurcation is discussed using the central manifold theory. Further, the global sensitivity analysis of the model is carried out using the Latin Hypercube sampling and the partial rank correlation coefficient techniques. Moreover, an optimal control problem is formulated and the necessary optimality conditions are investigated in order to eradicate the disease in a community. Four strategies are presented by choosing different set of controls combination for the disease minimization. Finally, the numerical simulations of each strategy are depicted to demonstrate the importance of suggesting control interventions on the disease dynamics and eradication.
World Health Organization declared the novel coronavirus disease 2019 (COVID-19) outbreak to be a public health crisis of international concern. Further, it provided advice to the global community that countries should place strong measures to detect disease early, isolate and treat cases, trace contacts and promote "social distancing" measures commensurate with the risk. This study analyses the COVID-19 infection data from the top 15 affected countries in which we observed heterogeneous growth patterns of the virus. Hence, this paper applies multifractal formalism on COVID-19 data with the notion that country-specific infection rates follow a power law growth behaviour. According to the estimated generalized fractal dimension curves, the effects of drastic containment measures on the pandemic in India indicate that a significant reduction of the infection rate as its population is concern. Also, comparison results with other countries demonstrate that India has less death rate or more immunity against 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.