Direct and indirect transmission of typhoid fever model with optimal control

Abstract In this paper, a model for direct and indirect transmission dynamics of typhoid fever with three control interventions is analyzed. Optimal control strategies are proposed to minimize both the disease burden and the intervention cost. We proved the existence and uniqueness of optimal control paths and obtained these optimal paths analytically using Pontryagin’s Maximum Principle. We analyzed our results numerically to compare various strategies of proposed controls. It is observed that the implementation of the three controls among all strategies is most successful. Thus, we conclude that in order to reduce typhoid fever threat, all the three controls must be taken into consideration concurrently.

[1]  Michael Y. Li,et al.  Modeling the effects of carriers on transmission dynamics of infectious diseases. , 2011, Mathematical biosciences and engineering : MBE.

[2]  B Cvjetanović,et al.  Epidemiological model of typhoid fever and its use in the planning and evaluation of antityphoid immunization and sanitation programmes. , 1971, Bulletin of the World Health Organization.

[3]  O. J. Peter,et al.  Modelling and optimal control analysis of Lassa fever disease , 2020 .

[4]  F. Marks,et al.  Typhoid fever vaccination strategies. , 2015, Vaccine.

[5]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[6]  Mustafa Bayram,et al.  Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative , 2021 .

[7]  Ghulam Hussain,et al.  Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan) , 2020, Results in Physics.

[8]  James M Hyman,et al.  Differential susceptibility and infectivity epidemic models. , 2005, Mathematical biosciences and engineering : MBE.

[9]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[10]  S. Mushayabasa.  A Simple Epidemiological Model for Typhoid with Saturated Incidence Rate and Treatment Effect , 2013 .

[11]  C. Poulos,et al.  An optimization model for reducing typhoid cases in developing countries without increasing public spending. , 2009, Vaccine.

[12]  Amir Khan,et al.  Model of rice blast disease under tropical climate conditions , 2021 .

[13]  E. Lifshitz.  Travel trouble: typhoid fever--A case presentation and review. , 1996, Journal of American college health : J of ACH.

[14]  F. A. Oguntolu,et al.  Direct and Indirect Transmission Dynamics of Typhoid Fever Model by Differential Transform Method , 2018 .

[15]  Ravi P. Agarwal,et al.  Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative , 2021, Mathematics.

[16]  G. Kang,et al.  Predicting the Impact of Vaccination on the Transmission Dynamics of Typhoid in South Asia: A Mathematical Modeling Study , 2014, PLoS neglected tropical diseases.

[17]  M. Khan,et al.  Mathematical analysis of typhoid model with saturated incidence rate , 2015 .

[18]  W. Edmunds,et al.  A review of typhoid fever transmission dynamic models and economic evaluations of vaccination , 2015, Vaccine.

[19]  Oluwole Daniel Makinde,et al.  Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies , 2017, Comput. Math. Methods Medicine.