Mathematical modelling and analysis of COVID-19 and tuberculosis transmission dynamics

Ram Singh; Attiq Ul Rehman; Tanveer Ahmed; Khalil Ahmad; Shubham Mahajan; Amit Kant Pandit; Laith Abualigah; Amir H Gandomi

doi:10.1016/j.imu.2023.101235

Mathematical modelling and analysis of COVID-19 and tuberculosis transmission dynamics

Inform Med Unlocked. 2023:38:101235. doi: 10.1016/j.imu.2023.101235. Epub 2023 Mar 31.

Authors

Ram Singh¹, Attiq Ul Rehman¹, Tanveer Ahmed², Khalil Ahmad², Shubham Mahajan^{3

4}, Amit Kant Pandit⁵, Laith Abualigah^{6

7

8

9

10

11}, Amir H Gandomi^{12

13}

Affiliations

¹ Department of Mathematical Sciences, BGSB University, Rajouri, 185234, India.
² Department of Mathematics, Al-Falah University, Faridabad, India.
³ Ajeenkya D Y Patil University, Pune, Maharashtra, 412105, India.
⁴ University Center for Research & Development (UCRD), Chandigarh University, Mohali, India.
⁵ School of Electronic and Communication, Shri Mata Vaishno Devi University, Katra, 182320, India.
⁶ Computer Science Department, Prince Hussein Bin Abdullah Faculty for Information Technology, Al al-Bayt University, Mafraq 25113, Jordan.
⁷ College of Engineering, Yuan Ze University, Taiwan.
⁸ Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman 19328, Jordan.
⁹ Faculty of Information Technology, Middle East University, Amman 11831, Jordan.
¹⁰ Applied science research center, Applied science private university, Amman 11931, Jordan.
¹¹ School of Computer Sciences, Universiti Sains Malaysia, Pulau Pinang 11800, Malaysia.
¹² Faculty of Engineering and Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia.
¹³ University Research and Innovation Center (EKIK), Óbuda University, 1034 Budapest, Hungary.

Abstract

In this paper, a mathematical model for assessing the impact of COVID-19 on tuberculosis disease is proposed and analysed. There are pieces of evidence that patients with Tuberculosis (TB) have more chances of developing the SARS-CoV-2 infection. The mathematical model is qualitatively and quantitatively analysed by using the theory of stability analysis. The dynamic system shows endemic equilibrium point which is stable when $R_{0} < 1$ and unstable when $R_{0} > 1$ . The global stability of the endemic point is analysed by constructing the Lyapunov function. The dynamic stability also exhibits bifurcation behaviour. The optimal control theory is used to find an optimal solution to the problem in the mathematical model. The sensitivity analysis is performed to clarify the effective parameters which affect the reproduction number the most. Numerical simulation is carried out to assess the effect of various biological parameters in the dynamic of both tuberculosis and COVID-19 classes. Our simulation results show that the COVID-19 and TB infections can be mitigated by controlling the transmission rate $γ$ .

Keywords: Bifurcation; COVID-19; Modelling; Optimal solution; Sensitivity analysis.