Modelling cystic echinococcosis and bovine cysticercosis co-infections with optimal control.

Cystic echinococcosis and bovine cysticercosis are diseases of economic importance especially to rural communities that earn their incomes from livestock. In this paper, a mathematical model for cystic echinococcosis and bovine cysticercosis co-infections is formulated and analyzed to determine parameters that drive the diseases and design the optimal control strategy. The basic reproduction number R 0 that governs the dynamics of cystic echinococcosis and bovine cysticercosis is computed by the next-generation matrix method, and the normalized forward sensitivity index is used to derive the sensitivity indices of model parameters. Sensitivity analysis shows that co-infections of cattle with cystic echinococcosis and bovine cysticercosis, open defecation rate by humans who are infected with taeniasis and the rate of slaughtering co-infected cattle play a significant role in the persistence of cystic echinococcosis and bovine cysticercosis. Sobol sensitivity analysis has been carried out to study global sensitivity of model parameters to state variables. The results show that the rate at which exposed dogs progress to infectious class, the rate at which humans who are exposed to taeniasis progress to infectious stage, the rate at which dogs are recruited, cattle per capita natural death rate, cattle recruitment rate and tapeworm eggs' natural death rate are the most sensitive parameters to exposed dogs, humans who are exposed to taeniasis, infectious dogs, infectious cattle, exposed cattle and tapeworm eggs in the environment respectively. The control strategies, such as cattle indoor keeping, meat inspection, and improved hygiene and sanitation are implemented in combination to determine the possibility of controlling the spread of cystic echinococcosis and bovine cysticercosis. The Pontryagin's maximum principle is applied to determine diseases' optimal control strategy. Results show that cattle indoor keeping and meat inspection are more effective in disease control when they are concurrently implemented. Rural communities that earn income from livestock can control cystic echinococcosis and bovine cysticercosis by reducing the number of cattle that are kept in free range system, inspect meat from cattle and improve hygiene and sanitation. [ABSTRACT FROM AUTHOR]