Mathematical Biosciences and Engineering, 2019, 16(2): 667-700. doi: 10.3934/mbe.2019032 Research article

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Modeling the impact of sanitation and awareness on the spread of infectious diseases

Rajanish Kumar Rai, Arvind Kumar Misra, Yasuhiro Takeuchi

1 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005, India
2 College of Science and Engineering, Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan

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Sanitation and awareness programs play a fundamental role and are much effective public health interventions to control the spread of infectious diseases. In this paper, a nonlinear mathematical model for the control of infectious diseases, such as typhoid fever is proposed and analyzed by considering budget required for sanitation and awareness programs as a dynamic variable. It is assumed that the budget allocation regarding the protection against the disease to warn people and for sanitation increases logistically and its per-capita growth rate increases with the increase in number of infected individuals. In the model formulation, it is assumed that the susceptible individuals contract infection through the direct contact with infected individuals as well as indirectly through bacteria shed in the environment. It is further assumed that a fraction of budget is used to warn people via propagating awareness whereas the remaining part is used for sanitation to reduce the density of bacteria. The condition when budget should spend on sanitation/awareness to reduce the number of infected individuals is obtained. Model analysis reveals that the sanitation and awareness programs have capability to reduce the epidemic threshold and thus control the spread of infection. However, delay in providing funds destabilizes the system and may cause stability switches through Hopf-bifurcation. Numerical simulations are also carried out to support analytical findings.

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