Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2406 
https://internationalpubls.com 

Solution of Ebola Virus Disease Outbreaks with Novel Technique 

Conformal Fractional Differential Transform Method 

 

C. Murugesan 𝟏, M. Dorthimary 𝟐,∗, G. Tamil Preethi 𝟑 And N. Magesh 𝟒. 

Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri-635001, 

Tamilnadu, India. 

e-mail:  1 cmurugesan27@gmail.com, 2,∗mdorthimary@gmail.com, 

 3 𝑡𝑎𝑚𝑖𝑙𝑝𝑟𝑒𝑒𝑡ℎ𝑖𝑔@𝑔𝑚𝑎𝑖𝑙. 𝑐𝑜𝑚  and   4nmagi_2000@yahoo.co.in 

 2,∗ORCID Address: https://orcid.org/0009-0000-9110-9308. 

 3 ORCID Address: https://orcid.org/0000-0003-3453-0029. 

 4ORCID Address: https://orcid.org/0000-0002-0764-8390. 

 

Article History: 

Received: 12-01-2025 

Revised: 15-02-2025 

Accepted: 01-03-2025 

Abstract:  

Differential Transform Method (DTM) is the new technique to solve the linear and 

nonlinear differential equations with initial and boundary conditions which provides the 

closest form of the exact solution. Conformable Fractional Differential Transform 

Method (CFDTM) is formulated for the fractional order power series in the same way. 

This paper deals with Ebola Virus Disease (EVD) epidemiological model of differential 

equations and applied CFDTM to the SIRDP (Susceptible-Infected-Recovered-

Deceased-Pathogens) model for different values of order 𝜁. By graphical representation, 

we can conclude that by taking immense measure in controlling the EVD by isolating 

the infected individuals from the environment and careful burial of deceased bodies. 

Mathematical calculations are done using Maple software to form the iterative series. 

2020 Mathematics Subject Classifications: 65L06, 92D25, 92D30. 

Keywords: Ebola Virus Disease (EVD), Conformable Fractional Differential Transform 

Method (CFDTM), Epidemiological Model- SIRDP. 

 

1. Introduction 

Ebola Virus Disease (EVD) is a severe disease caused by Ebola Virus, a member of the filovirus 

family, which occurs in humans and other primates. The disease emerged in 1976 in almost 

simultaneous outbreaks in the Democratic Republic of the Congo (DRC) and Sudan (now South 

Sudan). The largest outbreak took place in West Africa between March 2014 and June 2016, 

affecting primarily Guinea, Liberia and Sierra Leone over 28,000 cases were recorded. There are 

6 species of Ebola Virus and 4 of which have caused disease in humans. 

(1)  Zaire Ebola Virus (EBOV) 

(2) Sudan Ebola Virus (SUDV) 

(3) Tai Forest (TAFV) (formerly known as Ebola Ivory Coast) 



Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2407 
https://internationalpubls.com 

(4) Bundibugyo Ebola Virus (BDBV) 

The first human case is an Ebola outbreak is acquired through contact with blood, secretion organs or 

other body fluids of an infected animal. EVD has been documented in people who handled infected 

chimpanzees, gorillas and forest antelopes, both dead and alive in cote d’lvoire the Republic of Congo 

and Gabon. The virus is then transmitted from person to person through direct contact with blood, 

secretions, organs or other bodily fluids of infected through contact with objects such as needles or 

soiled clothing, that have been contaminated with infected secretions have been fuelled by traditional 

practices of burial, in which mourners have direct contact with the bodies of the deceased. Hospital 

workers have fully been infected during Ebola outbreaks through close contact with infected patients 

and insufficient use of correct infection control precautions and barrier nursing procedures. The 

primary symptoms of Ebola often includes fever, weakness and fatigue, sore throat, loss of appetite 

unexplained harmouaging, bleeding or bruising gastrointestinal symptoms including abdominal pain 

diarrhoea and vomiting and other symptoms include red eyes, skin rashes and hiccups (late stage) [2–

8, 10–13, 16]. 

A few of the numerical techniques for determining the solution of differential equations is the 

Differential Transform Method (DTM). Zhou is the first one to establish the DTM. He employed DTM 

to tackle linear and nonlinear initial value problems in electric circuit analysis [23]. A new analytical 

technique for solving fractional differential equations (FDEs) has recently been devised. Conformable 

Fractional Differential Transform Method (CFDTM) is a technique that formulates fractional power 

series in the same way as DTM formulates Taylor series. The conformable fractional differential 

transform method is being used to analyse fractional differential equations, fractional partial 

differential equations, fractional-order integro-differential equations and fractional differential-

algebraic equations [1, 14, 15, 17-21].  

In this paper, SIRDP(Susceptible-Infected-Recovered-Deceased-Pathogens) model is framed to 

get a numerical solution using Conformable Fractional Differential Transform Method (CFDTM) 

with their initial condition and parametric values. 

2. Conformable Fractional Differential Transform Method  

In order to expand the analytical and continuous function, 𝑓(𝑡) in terms of a fractional power 

series, we consider the basic definition and its properties of the conformable fractional one- 

dimensional differential transform method and studied by Ünal and Gökdoğan [22].  

Definition 2.1. [22] If we suppose that the function 𝑓(𝑡) is infinitely 𝛼 − differentiable function 

for some 𝛼 𝜖(0, 1], then the conformable fractional differential transform of 𝑓(𝑡) is defined as 

follows:  

                               𝐹𝛼(𝑘) =
1

𝛼𝑘 𝑘!
[(𝑇𝛼

𝑡0  𝑓)
(𝑘)
 (𝑡)]

𝑡=𝑡0
,                                                     (1)  

where (𝑇𝛼
𝑡0  𝑓)

(𝑘)
(𝑡) denotes the 𝑘𝑡ℎ iterate of the fractional derivative (𝑇𝛼

𝑡0  𝑓)(𝑡) for a function 

𝑓: (𝑡0, ∞) → ℝ given by 

          (𝑇𝛼
𝑡0  𝑓)(𝑡) ≔ lim

𝜀→0
{
𝑓(𝑡+𝜀(𝑡−𝑡0)

1−𝛼)−𝑓(𝑡)

𝜀
} ,           𝑡 ≥ 𝑡0 ≥ 0;    0 < 𝛼 ≤ 1.                  (2)                  



Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2408 
https://internationalpubls.com 

Definition 2.2. [22] If 𝐹𝛼(𝑘)  denotes the conformable fractional differential transform of the 

function 𝑓(𝑡) given by Definition 2.1, then the inverse fractional differential transform of 𝐹𝛼(𝑘)  

is defined by  

          𝑓(𝑡) = ∑𝐹𝛼(𝑘)

∞

𝑘=0

(𝑡 − 𝑡0)
𝛼 𝑘 = ∑

1

𝛼𝑘  𝑘!
[(𝑇𝛼

𝑡0  𝑓)
(𝑘)
 (𝑡)]

𝑡=𝑡0
(𝑡 − 𝑡0)

𝛼 𝑘

∞

𝑘=0

.            (3) 

By applying Definition 2.1 and 2.2, we are led to Definition 2.3 below: 

Definition 2.3.  [22] The conformable fractional differential transform (CFDT) of the initial 

conditions for integer-order derivatives are defined as follows: 

             𝐹𝛼(𝑘) = {
1

(𝛼 𝑘)!
[
𝑑𝛼 𝑘{𝑓(𝑡)}

𝑑𝑡𝛼 𝑘
]
𝑡=𝑡0

;                𝛼 𝑘 ∈ ℕ

  0;                                               𝛼 𝑘 ∉ ℕ
      for  𝑘 = 0, 1,⋯ , [

𝑛

𝛼
] − 1,        (4)        

where ℕ denotes the set of positive integers and 𝑛 is the order of the corresponding fractional 

differential equation. 

For properties one can refer [9, 14, 22]. 

3. Mathematical Formulation 

The Ebola virus in the habitat is classified into five compartments: susceptible population 

𝓈(𝑡), infected individuals 𝔦(𝑡), recovered 𝓆(𝑡), infected deceased 𝓌(𝑡) and the Ebola virus 

pathogen in the environment is classified as 𝔤(𝑡). Various equations have been used to explain the 

model and its behavior, including [15] 

𝑑𝓈(𝑡)

𝑑𝓉
= 𝛼1 − [𝛽1𝔦(𝑡) + 𝛽2 𝓌(𝑡) + 𝛾 𝔤(𝑡)]𝓈(𝑡) − 𝜍 𝓈(𝑡),                                     

𝑑𝔦(𝓉)

𝑑𝓉
= 𝛼2 + [𝛽1 𝔦(𝑡) + 𝛽2 𝓌(𝑡) + 𝛾 𝔤(𝑡)]𝓈(𝑡) − (𝜍 + 𝜃 + 𝜖)𝔦(𝑡),                  

                
𝑑𝓆(𝓉)

𝑑𝓉
= 𝜖 𝔦(𝑡) − 𝜍 𝓆(𝓉)                                                                                                        (5) 

 
𝑑𝓌(𝑡)

𝑑𝓉
= (𝜍 + 𝜃) 𝔦(𝑡) − 𝜔 𝓌(𝑡),                                                                                

        
𝑑𝔤(𝓉)

𝑑𝓉
= 𝜈 + 𝜒 𝔦(𝑡) + 𝜌 𝓌(𝓉) − 𝜉 𝔤(𝓉)                                                                         

Table 1. Parametric values for Ebola Virus Disease (EVD) [15]. 

Variable Description Values Variable Description Values 

α1 New Births 10 𝛾 Polluted environment 0.01 

α2 Infected neonate 3 θ Infectious human death 0.05 

β1 Susceptible infectious 0.006 𝜌 Deceased person rate 0.04 

β2 Diseased individuals 0.012 𝜍 Deceases person 0.5 



Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2409 
https://internationalpubls.com 

accumulated 

𝜈 Polluting environment 0 𝜖 Recovery rate 0.06 

𝜔 Rate of human burial 0.8 𝜒 Contagious rate 0.04 

 

4. Mathematical Modeling of the Conformable Fractional EVD Model 

            The conformable fractional model of real development of outbreak of infection in a 

huge population is given by the following conformable fractional differential system, 

                     𝑇𝜁  𝓈(𝓉) = 𝛼1 − [𝛽1𝔦(𝑡) + 𝛽2 𝓌(𝑡) + 𝛾 𝔤(𝑡)]𝓈(𝑡) − 𝜍 𝓈(𝑡),        

                     𝑇𝜁𝔦(𝑡) = 𝛼2 + [𝛽1 𝔦(𝑡) + 𝛽2 𝓌(𝑡) + 𝛾 𝔤(𝑡)]𝓈(𝑡) − (𝜍 + 𝜃 + 𝜖)𝔦(𝑡), 

                     𝑇𝜁𝓆(𝓉) = 𝜖 𝔦(𝑡) − 𝜍 𝓆(𝓉),                                                                                                  (6)  

                     𝑇𝜁𝓌(𝓉) = (𝜍 + 𝜃) 𝔦(𝑡) − 𝜔 𝓌(𝑡),  

                     𝑇𝜁𝔤(𝓉) = 𝜈 + 𝜒 𝔦(𝑡) + 𝜌 𝓌(𝓉) − 𝜉 𝔤(𝓉).                                                                          

                                                       

{
 
 

 
 
𝓈(0) = 3470                                                                                
𝔦(0) = 3317                                                                               

𝓆(0) = 2287                                                                         (7)

𝓌(0) = 1171                                                                                 
𝔤(0) = 0                                                                                      

 

 

4.1. Application of Conformable Fractional Differential Transform Method. 

        Equation (6) can be rewritten as follows:                                                                        

    𝜁(𝑝 + 1)𝒮𝜁(𝑝 + 1) =  𝛼1𝛿(𝑝)                                                                                                                    

 −∑𝒮𝜁(𝑟)

𝑝

𝑟=0

(𝛽1𝔗𝜁(𝑝 − 𝑟) + 𝛽2𝒲𝜁(𝑝 − 𝑟) + 𝛾𝒢𝜁(𝑝 − 𝑟)) − 𝜍𝒮𝜁(𝑝) 

𝜁(𝑝 + 1)𝔗𝜁(𝑝 + 1)

= 𝛼2 𝛿(𝑝)                                                                                                                                     

    −∑𝒮𝜁(𝑟)

𝑝

𝑟=0

(𝛽1𝔗𝜁(𝑝 − 𝑟) + 𝛽2𝒲𝜁(𝑝 − 𝑟) + 𝛾𝒢𝜁(𝑝 − 𝑟)) − (𝜍 + 𝜃 + 𝜖)𝔗𝜁(𝑝), 

𝜁(𝑝 + 1)𝒬𝜁(𝑝 + 1) = 𝜖 𝔗𝜁(𝑝) − 𝜍 𝒬𝜁(𝑝),                                                                                          (8) 

           𝜁(𝑝 + 1)𝒲𝜁(𝑝 + 1) = (𝜍 + 𝜃)𝔗𝜁(𝑝) −

𝜔 𝒲𝜁(𝑝),                                                                                   

    𝜁(𝑝 + 1)𝒢𝜁(𝑝 + 1) = 𝜈 𝛿(𝑝) + 𝜒 𝔗𝜁  (𝑝) + 𝜌 𝒲𝜁(𝑝) − 𝜉 𝒢𝜁(𝑝).                                                           



Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2410 
https://internationalpubls.com 

 Hence the recurrence relation is obtained as                                                                                        

𝒮𝜁(𝑝 + 1) =  
1

𝜁 (𝑝 + 1)
 [𝛼1𝛿(𝑝)  −∑𝒮𝜁(𝑟)

𝑝

𝑟=0

(𝛽1𝔗𝜁(𝑝 − 𝑟) + 𝛽2𝒲𝜁(𝑝 − 𝑟) + 𝛾𝒢𝜁(𝑝 − 𝑟)) 

− 𝜍𝒮𝜁(𝑝)]               

𝔗𝜁(𝑝 + 1) =
1

𝜁 (𝑝 + 1)
 [𝛼2𝛿(𝑝) +∑𝒮𝜁(𝑟)

𝑝

𝑟=0

(𝛽1𝔗𝜁(𝑝 − 𝑟) + 𝛽2𝒲𝜁(𝑝 − 𝑟) + 𝛾𝒢𝜁(𝑝 − 𝑟))

− (𝜍 + 𝜃 + 𝜖)𝔗𝜁(𝑝)] 

𝒬𝜁(𝑝 + 1) =
1

𝜁 (𝑝 + 1)
 [𝜖 𝔗𝜁(𝑝) − 𝜍 𝒬𝜁(𝑝), ]                                                                           (9)  

𝒲𝜁(𝑝 + 1) =
1

𝜁 (𝑝 + 1)
[(𝜍 + 𝜃)𝔗𝜁(𝑝) − 𝜔 𝒲𝜁(𝑝), ]                                                                        

 𝒢𝜁(𝑝 + 1) =
1

𝜁 (𝑝 + 1)
[𝜈 𝛿(𝑝) + 𝜒 𝔗𝜁  (𝑝) + 𝜌 𝒲𝜁(𝑝) − 𝜉 𝒢𝜁(𝑝) ].                                           

       Applying initial conditions (7) and parameter values from the table (1) we obtain the series for the 

         classical order   𝜁 = 1, upto certain order by inverse differential transform method as follows : 

 

𝓈(𝓉) =∑𝒮𝜁(𝑘)𝑡
𝑘𝜁

∞

𝑙=0

= 3470 − 116075.3800 𝓉 + 714521.3145 𝓉2 + 24337984.34 𝑡3 +⋯             

𝔦(𝑡) = ∑𝔗𝜁(𝑘)𝑡
𝑘 𝜁

∞

𝑙=0

= 3317 + 115800.0100 𝓉 − 778859.1625 𝓉2 − 24060529.42 𝓉3 +⋯        

𝓆(𝓉) =∑𝒬𝜁(𝑘)𝑡
𝑘 𝜁 =

∞

𝑙=0

2287 − 944.4800000 𝓉 + 3710.120300 𝓉2 − 16195.53663 𝓉3

+⋯  (10) 

𝓌(𝓉) =∑𝒲𝜁(𝑘)𝑡
𝑘 𝜁 =

∞

𝑙=0

1171 + 887.5500000 𝓉 + 31489.98275 𝓉2 − 151188.1752 𝓉3

+⋯          

𝔤(𝓉) =∑𝒢𝜁(𝑘)𝑡
𝑘 𝜁 =

∞

𝑙=0

179.5200000 𝓉 + 2331.058400 𝓉2 − 9988.232980 𝓉3 +⋯                        

 



Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2411 
https://internationalpubls.com 

 

5. Results and Discussion 

                The system of differential equations has been solved numerically to get approximate 

solutions.  

The solution is plotted using graphical representation. 

It is noted that the effectiveness of the EVD in the environment is due to the contamination from 

the infected people in the environment. There are a few preventive measures that can be adopted 

for the further spread of Ebola Virus Disease. Some of them are by 

(1) Avoiding contact with blood and body fluids such as urine, feces, saliva, sweat, vomit, breast 

milk, amniotic fluid, vaginal fluids of people who are sick. 

(2) Avoiding contact with semen from a man who has recovered from EVD until negative 

results. 

(3) Avoiding contact with an infected person’s blood and fluids in clothes, bedding, needles 

and medical equipment’s. 

(4) Avoiding funeral or burial practices that involve touching the body of someone who died 

from EVD or suspect EVD. 

(5) Avoiding contact with bats forest antelopes and non-human primates and by avoiding 

bushmeat. 

 

Figure 1. Graphical representation for vulnerable population  𝓼(𝓽) at time 𝓉 by CFDTM for 

different 

values of 𝜁. 



Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2412 
https://internationalpubls.com 

 

Figure 2. Graphical representation for vulnerable population  𝖎(𝓽) at time 𝓉 by CFDTM for               

different values of 𝜻. 

 

Figure 3. Graphical representation for vulnerable population  𝓺(𝓽) at time 𝓉 by CFDTM for          

different values of 𝜻.      

 

Figure 4. Graphical representation for vulnerable population  𝓺(𝓽) at time 𝓉 by CFDTM for 

different values of 𝜻. 



Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2413 
https://internationalpubls.com 

 

Figure 5. Graphical representation for vulnerable population  𝓖(𝓽) at time 𝓉 by CFDTM for 

different values of 𝜻. 

6. Conclusion 

A conformable fractional mathematical model for the spread of EVD has been proposed of presented. 

We have found out approximate solutions with the numerical method called CFDTM for the SIRDP 

model. This method is based on conformable derivative which is extremely popular in the last few 

years. The result reveals that to bring the Ebola Virus Disease under control infected person should be 

isolated from the environment and also by avoiding funeral and burial practices that involve touching 

the body of the died  EVD person and also the careful burial of them. 

REFERENCES 

[1] O. O. Acan, O. Firat and Y. Keskin, Conformable variational iteration method, conformable 

fractional reduced differential transform method and conformable homotopy analysis method for 

non-linear fractional partial differential equations, Waves Random Complex Media 30(2), 2020, 

250–268.  

[2] F. B. Agusto, M. I. Teboh-Ewungkem and A. B. Gumel, Mathematical assessment of the effect 

of traditional beliefs and customs on the transmission dynamics of the 2014 Ebola outbreaks, 

BMC Med., 13, 2015. 

[3] I. Area, H. Batarfi, J. Losada, J. J. Nieto, W. Shammakh and Á. Torres, On a fractional order 

Ebola epidemic model, Adv. Diff. Eq., 278 , 2015. 

[4] T. Berge, J. M. S. Lubuma, G. M. Moremedi, N. Morris and R. Kondera-Shava, A simple 

mathematical model for Ebola in Africa, J. Biol. Dyn., 11, 2017, 42-74. 

[5] K. Bibby, L. W. Casson, E. Stachler and C. N. Haas, Ebola virus persistence in the 

environment: State of the knowledge and research needs, Environ. Sci. Technol. Lett. 

American Chemical Society, 2, 2015. 

[6] G. Chowell, N. W. Hengartner, C. Castillo-Chavez, P. W. Fenimore and J. M. Hyman, The basic 

reproductive number of Ebola and the effects of public health measures: the cases of Congo 

and Uganda, J. Theor. Biol., 229, 2004, 119-126. 

[7] https://www.afro.who.int/health-topics/ebola-virus-disease, Ebola virus disease Democratic 

Re- public of Congo: external situation report 98/ 2020. 

http://www.afro.who.int/health-topics/ebola-virus-disease


Communications on Applied Nonlinear Analysis 

ISSN: 1074-133X 

Vol 32 No. 9s (2025) 

  

2414 
https://internationalpubls.com 

[8] D. Fisman, E. Khoo and A. Tuite, Early epidemic dynamics of the west african 2014 

Ebola outbreak: estimates derived with a simple two-parameter model, PLoS Curr., 6, 2014. 

[9] M. Hatami, D. D. Ganji and M. Sheikholeslami, Differential Transformation Method for 

Mechanical Engineering, Academic Press is an imprint of Elsevier, 2016. 

[10]  B. Ivorra, D. Ngom and Á. M. Ramos, Be-CoDiS: A Mathematical Model to Predict the 

Risk of Human Diseases Spread Between Countries—Validation and Application to the 

2014–2015 Ebola Virus Disease Epidemic, Bull. Math. Biol., 77, 2015, 1668-1704. 

[11] M. L. Juga, F. Nyabadza and F. Chirove,  An Ebola virus disease model with fear and 

environmental transmission dynamics, Infect Dis Model, 6, 2021,  545–559. 

[12]  E. M. Leroy, B. Kumulungui, X. Pourrut, P. Rouquet, A. Hassanin, P. Yaba, A. Délicat, J. T. 

Paweska, J.P. Gonzalez and R. Swanepoel, Fruit bats as reservoirs of Ebola virus, Nature, 438, 

2005, 575-576. 

[13]  E. M. Leroy, P. Rouquet, P. Formenty, S. Souquière, A. Kilbourne, J. M. Froment, M. Bermejo, 

S. Smit, W. Karesh, R. Swanepoel, S.R. Zaki and P.E. Rollin, Multiple Ebola Virus transmission 

events and rapid decline of Central African Wildlife, Science, 303, 2004, 387-390. 

[14]  M. Mamat, S. Syouri, I. M. Alghrouz, I. M. Sulaiman, S. F. Sufahani, Conformable Fractional 

Differential Transform Method for Solving Fractional Derivatives, International Journal of 

Advanced Science and Technology, 29  (7), 2020, 1734–1743. 

[15]  A. Nazir, N. Ahmed, U. Khan, S. T. Mohyud-Din, K. S. Nisar and I. Khan, An advanced 

version of a conformable mathematical model of Ebola virus disease in Africa, Alexandria 

Eng. Journal, 59, 2020, 3261-3268. 

[16]  A. Rachah and D. F. M. Torres, Mathematical Modelling, Simulation, and Optimal Control 

of the 2014 Ebola Outbreak in West Africa, Discrete Dyn. Nat. Soc., 2015, 1-9. 

[17]  R. Ross, The Prevention of Malaria, Dutton (1910). 

[18] R. Ross, H. Hudson, An application of the theory of probabilities to the study of a priori pathometry. 

Part II. Proceedings of the Royal Society of London. Series A, Containing Papers of a 

Mathematical and Physical Character. 93, 1917, 212-225. 

[19] G. Tamil Preethi, N. Magesh and N. B. Gatti, An application of conformable fractional 

differential transform method for smoking epidemic model, Mathematics and Computing 

(Springer Trends in Mathematics Book Series), 2023, 399 – 411. 

[20]  G. Tamil Preethi, B. C. Prasannakumara, N. Magesh and A. John Christopher, Multi-step 

differential transform method for solving epidemic model with pine wilt disease, Transactions of 

A. Razmadze Mathematical Institute, 177 (1) ,2023, 93 – 103. 

[21] G. Tamil Preethi and N. Magesh, An application of differential transform method to solve an 

epidemic model - Ebola virus disease outbreaks, Comm. Math. Appl., 14 (4) 2023, 1301–1310. 

[22] E. Ünal and A. Gökdoģan, Solution of conformable fractional ordinary differential equations via 

differential transform method, Optik Inter. J. Light Electron Optics, 218 2017, 264 – 273. 

[23]  J-K. Zhou, Transformation Differential and Its Application for Electrical Circuits. People’s 

Republic of China: Huarjung University Press, Wuhan; 1986.