Optimal control and effect of poor sanitation on modelling the acute diarrhea infection

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.

Modeling the effect of distancing and wearing of face masks on transmission of Covid-19 infection dynamics

“…The basic reproduction number, of the model system Eqs. (1-5) is obtained by using the next generation operator method, approach of [21] and is given below:…”

“…XGIJR model is the modification of SEIR model. In [21], the authors used SEIR model equations by incorporating time depend control and optimal control analysis. They used SEIR compartments to considered limited parameters, because they only focused at the trends, feeling, economic and political impacts caused by Covid-19 pandemic.…”

Model Epidemik Penyakit Diare Dengan Fungsi Insidensi Holling Tipe Dua

“…Penelitian-penelitian tentang penyakit diare melalui pemodelan matematika diantaranya: (Chaturvedi et al, 2018) membahas tentang model epidemik SIR dengan kompartemen I (Infected) dibagi menjadi dua kompartemen, (Bonyah et al, 2019) memperhatikan laju penularan dari manusia ke manusia, (Lasisi et al, 2020) memasukkan efek sanitasi pada model epidemik. Model-model ini sangat berguna untuk memahami hubungan berbagai kasus dan melakukan evaluasi terhadap upaya-upaya penanganan kasus-kasus epidemiologi.…”