Abstract
Taeniasis and cysticercosis pose a significant challenge to food safety and public health. Cysticercosis reduces the market value for pigs and cattle by making pork and beef unsafe for consumption. In this paper, a mathematical model for the transmission dynamics of taeniasis and cysticercosis in humans, pigs and cattle is formulated and analyzed. The analysis shows that both the disease free equilibrium (DFE) and the endemic equilibrium (EE) exist. To study the dynamics of the diseases, we derived the basic reproduction number R_{0} by next generation matrix method. When R_{0}< 1, the DFE is globally asymptotically stable whereas when R_{0} > 1 the EE is globally asymptotically stable. The normalized forward sensitivity index was used to determine sensitive parameters to the diseases. Humans’ recruitment rate, probability of humans’ infection with taeniasis and the defecation rate of taenia eggs by humans with taeniasis are the most positive sensitive parameters to diseases’ transmission whereas the human natural death rate is the most negative sensitive parameter. However, it is biologically unethical and not practical to increase human natural mortality rate for disease control. In this case, other parameters with negative sensitivity indices such as death rate of taenia eggs and proportions of unconsumed infected beef and pork can be considered for disease control. Generally, to control the diseases, more efforts should be made directed to reducing the number of humans who have taeniasis and defecate in the open environment. Also meat inspection and indoor keeping of cattle and pigs should be emphasized.
Highlights
Taeniasis and cysticercosis are foodborne infections which are caused by the adult and larval form tapeworms, respectively [29]
When humans who are infected with taeniasis defecate in the fields, the tapeworm eggs that are passed out with human faeces spread over the environment by several means, such as water, winds, animal feet and insects, and contaminate the soil, fodder, pastures and water sources [8]
The terms αp/(αp + δ) and αb/(αb + ) are the proportions of infected pork and beef that are eaten by susceptible humans, respectively, whereas γp and γc are the rates at which T. solium eggs and T. sagnata eggs are consumed by pigs and cattle, respectively, from the contaminated environment
Summary
Taeniasis and cysticercosis are foodborne infections which are caused by the adult and larval form tapeworms, respectively [29]. The terms αp/(αp + δ) and αb/(αb + ) are the proportions of infected pork and beef that are eaten by susceptible humans, respectively, whereas γp and γc are the rates at which T. solium eggs and T. sagnata eggs are consumed by pigs and cattle, respectively, from the contaminated environment. Since it is unethical and not practical to increase human natural mortality, other parameters with negative sensitivity indices such as death rate of taenia eggs and proportions of unconsumed infected beef and pork can be considered for disease control. The endemic equilibrium is a point at which taeniasis and cysticercosis exist in humans, pigs and cattle populations It is obtained by setting the derivatives in model system (1) equal to zero and solving for state variables. This indicates that human beings play an important role in transmission of the two diseases
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