A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

Abstract

A mathematical model for two strains of Malaria and Cholera with optimal control is studied and analyzed to assess the impact of treatment controls in reducing the burden of the diseases in a population, in the presence of malaria drug resistance. The model is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is proven not to exist. The necessary conditions for the existence of optimal control and the optimality system for the model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.

Optimal control strategies for the reliable and competitive mathematical analysis of Covid‐19 pandemic model

“…Since S(0) ≥ 0, so (9) implies that S( t) > 0 for all t ∈ [0, t 𝑓 ]. In the same way, we can prove that all the other state variables are positive.…”

“…In the field of mathematical modeling and optimal control design, researchers are continuously trying to develop different mathematical models of Covid-19 according to physical situations or requirements and are presenting a variety of control strategies for disease control. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] In this study, we design a new Covid-19 model termed as SEIAPHR where the infectious humans are placed in three compartments such as symptomatic infected I, asymptomatic A, and super-spreaders P. The division of infectious individuals in three compartments makes the model more realistic for the sake of analysis and control of disease. To restrict the spread of Covid-19 in human population, a few of nonpharmaceutical strategies such as quarantine, health awareness, self-protection, and social distancing are also proposed and incorporated in the Covid-19 SEIAPHR model.…”

“…Covid‐19 damages the human's lungs, liver, kidney, and so on. The mortality caused by Covid‐19 rates differently in different countries depending on the environment and food situation of the countries 1–3 , 4–12 . The mortality rate also relies upon the ratio of young and old people.…”

“…The mortality caused by Covid-19 rates differently in different countries depending on the environment and food situation of the countries. [1][2][3][4][5][6][7][8][9][10][11][12] The mortality rate also relies upon the ratio of young and old people. The people over the age of 60 and having diseases like diabetes, cancer, cardiac, obesity, blood pressure, and lungs issues are at high risk of getting a severe infection that may end up with death.…”

“…In the field of mathematical modeling and optimal control design, researchers are continuously trying to develop different mathematical models of Covid‐19 according to physical situations or requirements and are presenting a variety of control strategies for disease control 4–22 . In this study, we design a new Covid‐19 model termed as SEIAPHR where the infectious humans are placed in three compartments such as symptomatic infected $$$ I $$$, asymptomatic $$$ A $$$, and super‐spreaders $$$ P $$$.…”