Optimal control analysis of Taenia saginata bovine cysticercosis and human taeniasis

Bovine cysticercosis and human taeniasis are neglected food-borne diseases that pose challenge to food safety, human health and livelihood of rural livestock farmers. In this paper, we have formulated and analyzed a deterministic model for transmission dynamics and control of taeniasis and cysticercosis in humans and cattle respectively. The analysis shows that both the disease free equilibrium (DFE) and endemic equilibrium (EE) exist. To study the dynamics of the diseases, we derived the basic reproduction number R 0 by next generation matrix method which shows whether the diseases die or persist in humans and cattle. The diseases clear if R 0 < 1 and persist when R 0 > 1. The normalized forward sensitivity index is used to derive sensitive indices of model parameters. Sensitivity analysis results indicate that human's and cattle's recruitment rates, infection rate of cattle from contaminated environment, probability of humans to acquire taeniasis due to consumption of infected meat, defecation rate of humans with taeniasis and the consumption rate of raw or undercooked infected meat are the most positive sensitive parameters whereas the natural death rates for humans, cattle, Taenia saginata eggs and the proportion of unconsumed infected meat are the most negative sensitive parameters in diseases' transmission. These results suggest that control measures such as improving meat cooking, meat inspection and treatment of infected humans will be effective for controlling taeniasis and cysticercosis in humans and cattle respectively. The optimal control theory is applied by considering three time dependent controls which are improved meat cooking, vaccination of cattle, and treatment of humans with taeniasis when they are implemented in combination. The Pontryagin's maximum principle is adopted to find the necessary conditions for existence of the optimal controls. The Runge Kutta order four forward-backward sweep method is implemented in Matlab to solve the optimal control problem. The results indicate that a strategy which focuses on improving meat cooking and treatment of humans with taeniasis is the optimal strategy for diseases' control.

Modeling and dynamic analysis of novel coronavirus pneumonia (COVID-19) in China

Although novel coronavirus pneumonia (COVID-19) was widely spread in mainland China in early 2020, it was soon controlled. To study the impact of government interventions on the spread of disease during epidemics, a differential equation system is established to simulate the process of virus propagation in this paper. We first analyze its basic properties, basic reproduction number R 0 and existence of equilibria. Then we prove that the disease-free equilibrium (DFE) is Globally Asymptotically Stable when R 0 is less than 1. Through the analysis of the daily epidemic data from January 10, 2020 to March 11, 2020, combined with the implementation of the national epidemic policy, we divide the whole process into three stages: the first stage (natural state), the second stage (isolation state), the third stage (isolation, detection and treatment). By using the weighted nonlinear least square method to fit the data of three stages, the parameters are obtained, and three basic reproduction numbers are calculated, which are:R 01 = 2.6735 ,R 02 = 0.85077 ,R 03 = 0.18249 . Sensitivity analysis of threshold parameters and corresponding graphical results were also performed to examine the relative importance of various model parameters to the spread and prevalence of COVID-19. Finally, we simulate the trend of three stages and verify the theory of Global Asymptotic Stability of DFE. The conclusion of this paper proves theoretically that the Chinese government's epidemic prevention measures are effective in the fight against the spread of COVID-19. This study can not only provide a reference for research methods to simulate COVID-19 transmission in other countries or regions, but also provide recommendations on COVID-19 prevention measures for them.

Modeling and prediction of COVID-19 spread in the Philippines by October 13, 2020, by using the VARMAX time series method with preventive measures

COVID-19 outbreak is the serious public health challenge the world is facing in recent days as there is no effective vaccine and treatment for this virus. It causes 257,863 confirmed cases as of September 13, 2020, with 4292 deaths in the Philippines up till now. Understanding the transmission dynamics of the infection is a crucial step for evaluating the effectiveness of control measures. Owing to this, forecasts of COVID-19 cases, deaths, cases per million, and deaths per million are necessary for the Philippines. We examine the characteristics of COVID-19 affected populations based on the data provided by WHO from December 31, 2019, to September 13, 2020. In this paper, forecasts, and analysis of the COVID-19 cases, deaths, cases per million, and deaths per million were presented for 30 days ahead. The projection results are compared with the actual data values and simulated results from the VARMAX time series method. Societal growth is assessed by the median growth rate (MGR). President Rodrigo R Duterte of the Philippines has taken good steps but much more needs to be done. We suggest Philippines governments must rapidly mobilize and make good policy decisions to mitigate the COVID-19 spread. This paper mentions major contributions, current concerns, and challenges during and post COVID-19 epidemic in the Philippines with few non-considered measures to reduce the spread of the COVID-19.

The behaviour of infection, survival and testing effort variables of SARS-CoV-2: A theoretical modelling based on optimization technique

BACKGROUND

The experiences of SARS-CoV-2 are different in nature among the different states of the world. Studies on survival analysis of such pandemic mainly based on differential equation analysis, but the main limitation of such models is non-universal applicability. Consideration of improper functional relation in case of identification, survival and testing effort variables of the disease may be the cause of such non-universal applicability.

METHODS

Present study using optimization techniques try to find the general functional form for the variables like identification of the carrier's and testing effort. The study uses both the discrete and continuous time procedure of optimization technique. The main objective of the study is to institute relation between the identified carrier's and effort taken for identification.

RESULTS

The study considers test as the pseudo variable for effort of identification. The study found that the relationship between test and identified is not a linear one, rather it is nonlinear quadratic type. The study does not go for using data driven methods to verify the results.

Optimal control analysis of vector-host model with saturated treatment

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.