Abstract
Acute diarrhea disease has a greater threat to human population especially in poor sanitary or hygienic environments, which caused enormous mortality and mobility in the Society. In this paper, we proposed a model to describe the transmission of the acute diarrhea disease and optimal control strategies in a community. The reproduction number and global dynamics of the model are obtained. Global Stability of the Disease free and endemic state of the model equations is determined. It was found that, the Disease Free Equilibrium is globally asymptotically stable in feasible region Ω if R0≤1 and Endemic state is globally asymptotically stable when R0>1. The Optimal control problem is designed with two control strategies, namely, the prevention through minimizing the contact between the infected with acute diarrhea infectious and susceptible, and treatment of an individual. The existence of optimal control model is obtained. Numerical results of the dynamics of the disease are presented. It was found that, as the effective contact rate increases, it increases the reproduction number of the model equations, also as the effectiveness of compliance of good hygiene increases, it decreases the reproduction number of the model by varying the contact rate and more so, as production rate of acute diarrhea bacteria increases, it increases the secondary cases of the infected individuals.
Highlights
Acute diarrhea is one of the most common reported illnesses in developing Country, according to World Health Organisation (WHO), it is second leading cause of mortality in children young than four years old, in the developing world
Diarrhea infection which may lasts less than 2 weeks is known as acute diarrhea, while, Chronic diarrhea lasts longer than 4 weeks
Recovery class (R): this class includes all individuals that have recovered from the infection and move back to susceptible and Concentration of Bacteria is C, as shown in Fig. 1, C is interact with population X as it shown with dash arrow and become infected I with tick line, I recovered and move to Recovery class R, R have only temporary recovery, it move back to X, X is vaccinated and move to vaccination class and vaccination win out an become susceptible (X) again
Summary
Acute diarrhea is one of the most common reported illnesses in developing Country, according to World Health Organisation (WHO), it is second leading cause of mortality in children young than four years old, in the developing world. Mortality from acute diarrhea is globally declining but remains high in developing Country. Most estimates considered diarrhea infection as the second cause of childhood mortality, with 18 % of the 10.6 million yearly deaths in children younger than age 5 years [1]. The Human Immunodeficiency Virus (HIV) [5,6,7] These models have been helpful to study the control of the virus kinetics in order to provide a quantitative understanding and create public awareness of the ISSN PRINT 2538-7995, ISSN ONLINE 2538-8002, KAUNAS, LITHUANIA. OPTIMAL CONTROL AND EFFECT OF POOR SANITATION ON MODELLING THE ACUTE DIARRHEA INFECTION. With the scarcity of data and no literature review on acute diarrhea infection, the assumptions and estimation of the values of the parameters of the model would be considered
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